# A Level Physics: Specific Heat Capacity Question examples from past papers (2023)

## Introduction

Practice Past Paper questions on specific heat capacity.

I strongly recommend working through the video by pausing at the appropriate times to attempt the question and then check your solution.

Full list of official OCR Past Paper questions and solutions can be found at the OCR official website:
www.ocr.org.uk/qualifications/past-paper-finder/

## Video

In this video we're going to look at some specific heat past paper question, examples, we're going to start with a multiple choice question.

This is a multiple choice question from 2018, ocr physics, a modeling physics and question, three in particular, okay.

So without any further ado, let's have a look.

We've got a metal block of mass 0.28 kilograms.

It has some sort of an initial temperature.

Then we drop it into cold water.

So it's going to be losing some of that thermal energy away.

The temperature of the block after 1.2 minutes is 20 degrees c.

And we have the specific heat capacity of the metal being 130 joules per kilogram per kelvin.

What is the average thermal power transferred away from the metal block? Okay, this will be a perfect time for you guys to pause, this video and attempt this question, independently, perfect.

I chose that all of you guys have done this.

Now let's have a look at the solution.

My first step will be to write down the equation for power because that's what I'm looking for.

So we can just say the power is energy, divided by time like so our energy is going to be mc multiplied by our change in temperature, delta, theta, divided by the time.

Our mass is 0.28 kilograms.

So we can write that as 0.28 we're given the specific heat capacity c in in our si units already so no need of any conversion.

So we can just write multiply by 130 our change in temperature.

If the block is going from 82 degrees to 20 degrees is going to be 62 degrees.

So 62 divided by the time.

Now, in this case, that's 1.2 minutes, so I'm just going to be a little bit careful I'm going to make sure that I convert that to seconds.

So the way we do that is we just write down 1.2 multiply by 60.

And if we put those numbers into a scientific calculator, the correct answer up to two significant figures is going to be 31 watts.

And we can see that this is this is answer a so that's, the correct answer in this case, a perfect.

Now let's have a look at a written question in particular.

This is a question from 2013.

So it's a slightly older question.

We've got a room which measures four and a half times four times 2.4 meters.

And the air in the room is heated we're, given the change in temperature, given the density of the s we'll probably be able to work out the mass.

And the first part is asking us for the thermal energy.

Okay.

Now this will be the perfect time for you guys to pause this video and fully attempt those five marks.

Okay, I'm sure that everyone here has paused the video and attempted those questions.

Independently.

Just as you should have now let's go for the solution.

Okay, calculate the thermal energy required to raise the temperature of the air in the room I'm just going to write on the side, the equation for it.

So the equation is that the energy is equal to m, c, delta, theta, where theta is my change in temperature.

Now, I'm, not given the mass.

You can work that out from the density.

I am given the specific heat capacity over here.

And I am given the change in temperature.

Okay.

So in order to find the thermal energy, the first thing I would need to do is find my mass.

Now, if I'm given the density I'm just going to start off with the equation for for density.

So you know, the density is mass over volume, which means that mass is given by density times volume.

Now if we plug in some numbers into this, our density is 1.3 kilograms per meter.

So she'll just write that down over here.

So it's going to be 1.3 multiplied by the dimensions of the room.

So that's going to be 4.5 multiplied by four point zero times, two point, four and that's going to give us our mass in kilograms and the correct answer for that is 56.2.

Now remember I'm not really doing any rounding at this stage, not doing any any rounding and I'm going to just put the answer the correct number of significant figures as the final step in my calculation.

Okay.

So now that I have the mass, I can plug this back into the equation, which I wrote on the right hand side.

So the, um energy will then be given by the mass, which is 56.2 so 56.2 multiplied by the specific heat capacity, which is 990 so times 990.

And finally, my change in temperature, which is just 21 minus 12 degrees perfect.

And uh, if we were to plug this, these numbers into our scientific calculator up to two significant figures, I'm going to get an answer of 5.0 times 10 to the 5, joules perfect.

Now we can see our mark distribution.

In this case, we're marking this as an ocr examiner.

Our first mark is going to go for finding the mass of the air.

So if you've done this give yourself a mark, if you've given the substitution mark, which is this one over here for the energy, give yourself another mark.

So you have two out of three.

And finally, if you're given the correct answer, which is 5.0 times 10 to the 5, give yourself another mark perfect.

Now, the next bit of the question is asking us to calculate the time required to raise the temperature of the room from 12 to 21 degrees.

Okay.

Well, in this case, we are given the power.

So what I'm going to do is just write down my equation for power.

We like this equation.

So power is just energy over time.

Now, all I need to do then is just rearrange this equation for time.

So let's do that so time will be energy divided by power, which I can now substitute my values directly.

I've already I've already found the energy and the question above 5.0 times 10.5 so I'm just going to input that back here.

Okay.

So let's do that 5.0 times 10 to the 5 and divided by the power, which is 2.3 kilowatts.

Now remember 2.3 stands for, um 2.3 times 10 to the 3.

So let's just write that down so it's going to be 2.3 times 10 to the 3 watts.

And if we divide those two numbers once again, up to two significant figures, we're going to get 220 seconds perfect so I'm going to make sure I put my answers on here.

So it's going to be 220 seconds in this box and 5.0 times 10 to the 5 in the box above the mark distribution for this one is the substitution mark, which is this one over here and the correct final answer.

Okay, guys.

Now let's have a look at the rest of the question once again.

So let me just scroll down to it.

This would be a perfect time.

Just pause, this video and attempt the rest of the question.

Okay, perfect.

So, uh, moving on what the next part part I I is asking us to do is to calculate the mass of the heating gas.

Now, this is not the mass of the air.

This is the mass of the heating gas of the um, the hit of the heater.

So it says over here that each cubic meter of heating gas provides 39, mega joules of thermal energy.

Well, hang on a minute we're, actually given that the total thermal energy here was 5.0 times 10 to the 5 joules.

So if I divide this by 39 megajoules, I should be able to get the volume of the heating gas.

Okay, so let's just write this down.

So, um, let's divide this so it's going to be 5.0 divided by 39 times 10 to the 6, remember, um, mega stands for 10 to the power of 6, oops let's, not forget times 10 to the 5, just above so that's going to be the volume of my heating gas and we'll just write that down on the side.

So the volume of the let's say of the heating gas like so so it's 5.0 times century, five divided by 39 times 10 to the six.

We put that into a calculator we're going to get no point, uh, not one to eight cubic meters perfect.

Uh, the answer kind of makes sense as well, it's, not something terribly big.

So so far so good, um, we're already, given the density of of this gas up here.

So it's, 0.72 kilograms per meter.

So we can just directly calculate the mass of our gas.

So we can just say that mass is density times volume once again, and we can just input those numbers.

So a density is no 0.72 and our volume as we calculated just up.

There is going to be no point, not one two eight.

If we put those two numbers into our trusted scientific calculator for our mass we're, going to get nine point two times ten to the power of minus three mark spread for this question, as you can probably guess there's, a total of two marks available.

One is going to go for finding the volume of the gas.

So you can give yourself a tick if you've done this quite a lot of students, nationwide did not actually get this mark.

So it was, it was a tricky one.

And once we had this the second mark goes for calculating the mass okay, perfect.

Now very last bit suggests two reasons why the time required and the mass of the heating gas will in practice, be greater than the values calculated in part b.

Well, this question is all about thermal energy, which is being lost now this one thing and I cannot stress this enough is that exam boards do not really like as um bold, statements, such as heat lost to the surroundings, even though it's true, what we need to do is more specific.

So we need to be a little bit more specific.

So what I would, um, so I need to give two reasons for two marks for my first reason, I'm going to say that thermal energy was lost.

So let's just write this down.

So thermal energy was lost let's say to the walls of the room.

It could be the walls of a container or anything like that to the walls of the room in practice, uh, you could probably also write, um, if there's a you know that it could be windows, or it could be lost through the floor or anything else.

And finally, I also say that probably some objects, um in the room.

So probably thermal energy was, uh lost to other objects within the room.

So so thermal energy was lost to other objects.

So thermal energy was lost to other objects in the room.

Just here on the side, I'm going to write down a third possible mark now, I'm going to write this in red as well.

Because this is just another option by doing by writing those two.

We've already gotten the full marks.

However, we could also have written that some air may escape actually the room.

This room is is probably not perfectly sealed.

So that would mean that, um, some massive air may escape the room.

So some massive air may escape room.

You can kind of think of this as a container, which is just not perfectly sealed.

Okay, guys.

So hopefully you've enjoyed this past paper question.

Video, if there are any questions any questions on the question, feel free to drop a.

## FAQs

### What are some solved examples of specific heat capacity? ›

The specific heat capacity of copper is 390 J/kg-1°C-1. Example: A 250g block of Aluminium is heated in a water bath to 100°C. After being placed in 300g of 21.0°C water, the temperature of the water rises to 331°C.

What are examples of specific heat capacity in physics? ›

The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg1⋅K1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg1⋅K1.

What is specific heat capacity answers? ›

The specific heat capacity is defined as the amount of heat energy necessary to change a given amount of a substance by a certain temperature.

What is an example of specific heat capacity of water in real life? ›

For example, if you're at the beach on a sunny day, you'll notice that the sand is often quite hot to walk on, but the water always feels cool, even in the shallows. That's because sand has a lower specific heat capacity—it takes less energy to raise the temperature by one degree.

What is an example of calculating specific heat? ›

Example of Using Specific Heat to Calculate the Amount of Heat Energy Added to a Substance. A 250-gram cube of aluminum is heated from 20 degrees centigrade to 40 degrees centigrade. How much energy was required to heat the aluminum? The specific heat of aluminum is C p = 0.89 J g ⋅ ∘ C .

What is an example of a specific heat? ›

specific heat, the quantity of heat required to raise the temperature of one gram of a substance by one Celsius degree. The units of specific heat are usually calories or joules per gram per Celsius degree. For example, the specific heat of water is 1 calorie (or 4.186 joules) per gram per Celsius degree.

What does Q MCAT stand for? ›

Q=m⋅c⋅△T. where. Q stands for the quantity of energy (J) m stands for the mass of the substance (g) c stands for the specific heat capacity of the substance, which is the quantity of energy supplied to 1 g of this substance to raise its temperature by 1 ∘C 1 ∘ C (J/(g⋅°C))

What is specific heat capacity physics a level? ›

Specific heat capacity is the amount of heat (in joules) required to raise the temperature of 1kg of a substance by 1 kelvin. Its unit is J per kg per kelvin. The formula for specific heat capacity is c = Q / (mΔT), where “c” is the specific heat capacity.

What is one daily life example of heat capacity? ›

When you heat up a pot of water on the stove, which one heats up first: the pot or the water? The pot heats up faster! Although you are putting the same amount of heat on both substances, the pot responds quicker than the water because water has a high heat capacity.

How do you calculate heat capacity? ›

The amount of heat gained or lost by a sample (q) can be calculated using the equation q = mcΔT, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change. Created by Jay.

### Does specific heat capacity change with temperature? ›

In general, heat capacity depends on temperature, so the answer is no, the amount is different. However, due to the equipartition theorem, at sufficiently high temperature (compared to the typical temperature scale given by quantum mechanics) the temperature dependence flattens out.

What is the meaning of ∆ T in physics? ›

a = acceleration ∆v = change in velocity ∆t = elapsed time The definition of acceleration.

Can specific heat be negative? ›

When heat is absorbed from the system, q is negative. So specific heat will be negative.

Can heat capacity be negative? ›

If a temperature is defined by the average kinetic energy, then the system therefore can be said to have a negative heat capacity. A more extreme version of this occurs with black holes. According to black-hole thermodynamics, the more mass and energy a black hole absorbs, the colder it becomes.

How much water is specific heat? ›

The specific heat of water is 1 calorie/gram ∘C = 4.186 joule/gram ∘C which is higher than any other common substance.

Why is water high specific heat? ›

Water has a higher specific heat capacity because of the strength of the hydrogen bonds. It requires a significant of energy to separate these bonds.

What is the specific heat of water with temperature? ›

Water has a specific heat capacity of around 4.2 J/g°C. As a result, raising 1 gram of water by 1°C requires 4.2 joules of energy. The heat required to increase the temperature of a particular substance's unit mass by a certain quantity is referred to as its specific heat capacity.

What is the easiest way to calculate specific heat? ›

Subtract the final and initial temperature to get the change in temperature (ΔT). Multiply the change in temperature with the mass of the sample. Divide the heat supplied/energy with the product. The formula is C = Q / (ΔT × m) .

What is the basic formula of specific heat? ›

Specific heat is the quantity of heat essential to raise the temperature of one gram of any substance by 1 degree Celsius. The temperature difference is given by Δ T = (Tf – Ti), where the final temperature is Tf and the initial temperature is Ti .

How much heat is required to raise the temperature? ›

The equation for the amount of heat, Q , required to change the temperature of an object in a single phase is Q = m c Δ T , where m is the mass of the substance, c is the specific heat capacity of the substance, and Δ T is the change in temperature of the substance.

### What are 5 examples of heat? ›

Heat Energy Examples
• The Sun is the biggest source of heat energy in our solar system. ...
• A stovetop acts as a source of heat energy when it burns the gas. ...
• Automobile fuels are also a source of heat energy. ...
• A hot cup of tea or coffee contains heat energy.

What is heat in real life example? ›

Heat is used to make things warm, to boil water and fry eggs and to melt metal to build cars. Heat is used to generate electricity at a thermal power plant for our daily lives. Temperature is the measure of how hot or cold matter is.

What are the 4 MCAT scores? ›

Each of the four sections of the MCAT is scored between 118 and 132, with the mean and median at 125. The total MCAT score range is between 472 to 528, with the mean and median at 502.

What is the highest and lowest MCAT? ›

MCAT Score Range

Each MCAT section is scored on a scale of 118–132 (highest). Your MCAT total score (whch is the sum of your section scores) ranges from 472–528. Because different versions of the test have varying levels of difficulty, the scale will be slightly different from one MCAT administration to the next.

What does C mean in specific heat? ›

Hence, the term “C” in stands for specific heat capacity.

What is 1 specific heat capacity? ›

The specific heat capacity is defined as the quantity of heat (J) absorbed per unit mass (kg) of the material when its temperature increases 1 K (or 1 °C), and its units are J/(kg K) or J/(kg °C).

What is the formula for specific heat capacity with power? ›

C = Q / (∆T m) is the formula. Answer: The heat or energy required during a constant volume process to change the temperature of a substance of unit mass by 1 °C or 1 °K is measured in J/kg K or J/kg C, as it is the heat or energy required to alter the temperature of a substance of unit mass by 1 °C or 1 °K.

What is the formula for rearranging specific heat capacity? ›

This equation can be rearranged to solve for the specific heat. c=QmΔT Thus, to calculate the specific heat of a substance we must transfer a known amount of heat into a known mass, and measure the change in temperature.

What factors affect specific heat capacity? ›

This quantity is known as the specific heat capacity (or simply, the specific heat), which is the heat capacity per unit mass of a material. Experiments show that the transferred heat depends on three factors: (1) The change in temperature, (2) the mass of the system, and (3) the substance and phase of the substance.

What is the specific heat capacity of water 4180? ›

The specific heat capacity of water is 4180 J kg-1 K-1.

### What is the formula for specific heat capacity at constant volume? ›

The specific heat at constant volume for a gas is given as (∂U∂T)V=cv.

Does water or sand have a higher heat capacity? ›

Those in the water are most likely feeling cooler than those on the sand. This is due to the high specific heat capacity of water. In other words, the same amount of heat energy when applied to sand and water will increase the temperature of the sand more than it will increase the temperature of the water.

What as an example of heat and heat expansion you experience in everyday life? ›

Other examples of thermal expansion include: - The air in a car tyre gets warm after a long journey and this increases its pressure. - Railway lines require expansion gaps (similar to bridges) to avoid buckling in hot weather.

What as an example of heat and heat expansion you experience in every day life? ›

The most visible example is the expansion of hot air. When air is heated, it expands and becomes less dense than the surrounding air, which then exerts an (upward) force on the hot air and makes steam and smoke rise, hot air balloons float, and so forth.

What does Q stand for in Q MC ∆ T? ›

The formula below is used to calculate the amount of energy absorbed/released during calorimetry. q = mc∆T. where q = heat (in joules); m = mass (in grams); c = specific heat (in joules/grams • °C); ΔT = change in. temperature (i.e. final temp – initial temp) (in °C or K)

How much energy is needed to change the temperature of 50.0 g of water by 15.0 OC? ›

Answer and Explanation: It will take 3 , 139.5 J o u l e s to change the temperature of 50.0 g of water by 15.0 ∘ C .

Why does heat capacity go to zero? ›

As the temperature approaches absolute zero, the specific heat capacity of a system also approaches zero, due to loss of available degrees of freedom due to the quantum mechanical effect.

How does pressure affect heat capacity? ›

In model calculations, heat capacity increases with pressure, decreases, or remains insensitive to pressure, depending on the model applied. The expression cannot be applied to the gases, but experimental data on gases show evidently that heat capacity increases with pressure.

Does specific heat capacity depend on mass? ›

Statement 2: Specific heat capacity of a substance is independent of mass of substance.

What has the highest specific heat? ›

Water has the highest specific heat capacity of any liquid. Specific heat is defined as the amount of heat one gram of a substance must absorb or lose to change its temperature by one degree Celsius.

### Is heat capacity always positive? ›

Molar specific heat capacity of a gas can be negative, positive or zero.

Does higher specific heat mean higher temperature? ›

Water has a high specific heat, meaning it takes more energy to increase the temperature of water compared to other substances.

What is specific heat capacity used for in real life? ›

The specific heat capacity of solids is used primarily in the construction industry for the assessment of the behavior of building material. In summer, fabrics with high heat capacity keep the rooms cool for a long time. In winter, they keep the heat in the buildings longer.

What are examples of specific heat in science? ›

Specific heat is defined by the amount of heat needed to raise the temperature of 1 gram of a substance 1 degree Celsius (°C). Water has a high specific heat, meaning it takes more energy to increase the temperature of water compared to other substances.

Which substance has a specific heat capacity? ›

Water has the highest specific heat capacity.

What are the three uses of specific heat of water in daily life? ›

Explanation: Fomentation: Hot water bottles are used for fomentation, as the water remains hot in the bottle for a long time in spite of giving off large quantities of heat. Car radiators: Water is used as coolant car radiators. Bottled Wines: In cold countries, wine bottles re kept under water.

Why does specific heat increase with temperature? ›

As the substance heats up, the average kinetic energy of the molecules increments. The collisions confer enough energy to permit rotation to happen. Rotation at that point adds to the interior energy and raises the specific heat.

What are the 10 examples of heat? ›

Heat Energy Examples
• The Sun is the biggest source of heat energy in our solar system. ...
• A stovetop acts as a source of heat energy when it burns the gas. ...
• Automobile fuels are also a source of heat energy. ...
• A hot cup of tea or coffee contains heat energy.

What is heat examples in daily life? ›

The sun radiates heat to warm us up on the planet earth. When the burner of a stovetop is very hot, it is a source of heat energy. Anything placed onto the stovetop and warmed, whether a pot of tea or a skillet for frying eggs, also become sources of heat energy.

What is an example sentence for specific heat? ›

Because of their high specific heat, these dressings are cooling to the skin, aiding in pain control and reducing inflammation. Copper is used because of its very high specific heat conductivity and to its high catalysis. We use a specific heat ratio of 1.4 for all gases.

### What has highest heat capacity? ›

Water has the highest specific heat capacity.

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