# Simple question about the heat, temperature and volume

Here I have one question taken from one test paper of a junior-high school in Asia:

(sorry, my English may not be clear enough):

In case with an amount of water being equal to 10 grams and its temperature being +5°C, which one of the following statements is correct:

A) the amount of water contains 50 calories of heat;

B) for its temperature to be increased by 1 degree (Celsius), this amount of water will need to absorb 10 calories of heat;

C) compared to a one-gram amount of water of the same temperature (+5°C), it contains more heat;

D) all three previous statements are true;

The paper states that I need to choose only one option, the correct one.

My logic regarding this question went like this:

50 calories is the amount of heat it would need to lose to go down to 0°C in temperature. However, if I cool this amount of water down to 0°C, it still won’t mean that there will be no heat left in it (0°C is not the absolute zero, the molecules and atoms will still be moving in it, which means some energy, that is, heat, will still be in it). Thus, the original amount (10 grams, +5°C) must contain more than 50 calories of heat. So the statement A is false. And, therefore, statement D is also false;

The definition of a calorie states that “one calorie is the amount of heat energy needed to raise the temperature of one gram of water by one degree Celsius”. So, if the amount is ten times bigger (that is, 10 grams), then 10 calories would be needed. So, the option B is correct.

Naturally, I would just choose option B in such cases and totally disregard option C, but then I looked at option C and was kind of puzzled. It looks to me that the statement in option C is also correct! It says that “compared to a one-gram amount of water of the same temperature (+5°C), it contains more heat”. It looks absolutely correct to me. But if it’s correct, then how can I “choose only one option, which the correct one”? So, where am I mistaken?

(The teacher’s note on paper was saying that the correct answer is B, but I still don’t understand why C is wrong)

• You are confusing the physical concept of heat (which is NOT a property of a body but a measure of transferred energy) and internal energy. You may find useful answers to simiiar questions like this physics.stackexchange.com/q/474282 Dec 22, 2019 at 9:29
• @GiorgioP - Thank you. Can you, please, quickly say if option C is wrong? Dec 22, 2019 at 9:31
• @GiorgioP - While from your link I gather that there is a difference between internal energy and heat, which is transferred energy, it doesn't help me much in understanding the nature of one and the nature of the other because that link talks about a human body, which is an organism, while in my question I am dealing only with water. So, the option C is also wrong, right? I am now more confused then before. If some energy was transferred into one object, does it contain that transferred energy now or not? If it does, then does it become its internal energy? If not, why not? Dec 22, 2019 at 9:50
• In physics using the English language "heat" is always a verb and not a noun, the infinitive to heat some material body makes sense, but a body does not contain heat as the body itself is the linguistic object of the verb. Just like one can read a book, but the object here is the book that does not contain read instead it contains pages. What may happen in the everyday language, not physics, is another story. Dec 22, 2019 at 14:31

Heat is energy transfer due solely to temperature difference. Note the emphasis on "energy transfer". Things do not "contain" heat. The energy contained or stored in things is properly called "internal energy".

Simply put, choices A and C violate the definition of heat. The energy "contained" in the water is its internal energy, which is the sum of its microscopic kinetic and potential energy. It is not heat. What's more, the temperature of the water only relates to its internal kinetic energy. It does not account for the internal potential energy of the water.

Can you, please, elaborate on "which is the sum of its microscopic kinetic and potential energy"? Could it be correct to say that internal energy pertains to microscopic processes while heat pertains to macroscopic ones? Microscopic is between atoms, molecules, particles, etc within a system. Macroscopic is between systems.

Heat and work are energy transfer between systems (in thermodynamics, normally referred to as between a system and its surroundings). The consequence of the energy transfer can be a change in the microscopic internal energy of systems involved in the transfer. The relationship between heat, work and internal energy is given by the first law.

Hope this helps.

• Thank you for your answer. Can you, please, elaborate on "which is the sum of its microscopic kinetic and potential energy"? Could it be correct to say that internal energy pertains to microscopic processes while heat pertains to macroscopic ones? Dec 22, 2019 at 12:37
• @brilliant Please elaborate as to what you mean by "microscopic process" vs a "macroscopic process". Dec 22, 2019 at 12:43
• Microscopic is between atoms, molecules, particles, etc within a system. Macroscopic is between systems. Dec 22, 2019 at 12:50
• @brilliant OK. See update to my answer. Hope it helps. Dec 22, 2019 at 14:35

Wikipedia starts its definition of heat by saying "[...] heat is energy in transfer [...]". I emphasised "in transfer", because this seams to be the key point you are missing. Heat is a quantity, which we do not (!) store in a system.

Taking your example, we know that water at $$5°C$$ contains a certain amount of energy. However, this energy is not stored as "heat", but as so called internal energy: The particles are moving in the liquid, they are rotating, they are vibrating (only at "high" temperature), and there exists binding-forces between the molecules.

Why is it useful to split energy into different categories (e.g. heat, work, internal energy)? Well, suppose you have water @ room temperature and you would like to bring it to 80°C. The amount of (internal) energy stored in the water @ 80°C is always the same, however, there are efficient ways to heat up the water and there are inefficient ways. Therefore, the amount of heat you are using to fulfil your goal is not constant. Thus, internal energy describes the amount of energy which we associate with the state of the system (e.g. water @ 5°C). In contrast, heat is only present if we transfer the system from one state (e.g. $$T_1=5°C$$) to another state (e.g $$T_2=0°C$$).

If I take a crowbar and transfer a whole lot of heat into it by means of holding its end out over a fire to the point when it starts glowing red, you may still say that it doesn’t store in its system the heat that has been transferred into it, but I will still not dare touch it because I know that now it contains a lot more heat [energy] that it contained before.

The key point is, that it does not contain heat, but energy. We use the word "heat" only if we are describing the transition of energy between two state. Neither the initial nor the final state contains heat. They only contain energy. This might seam as a play of word, however, there is much more behind it -- there is a hole semester at university level, where this is explained.

So if it’s the internal energy, then what will happen to it if I cool that water down to +1°C? Will that mean that some part of its internal energy be gone now?

The answer is Yes: If the internal energy changes, we change the temperature of the system as well. There exists direct relationship between temperature and internal energy. It state that $$U = constant \cdot T$$, where $$U$$ is the internal energy and $$T$$ is the temperature.

If yes, that is, the internal energy can be turned into transferred energy, then why transferred energy cannot be transferred into internal one?

The answer to your second question is given by the first law of thermodynamics. It reads $$\Delta U = W + Q$$ This means, that the change of internal energy $$\Delta U$$ is equal to the amount of work $$W$$ done by the system on it's surrounding, and the amount of heat $$Q$$ supplied by the surrounding to the system. So the answer to your question is yes again: Internal energy can be transferred into heat and heat can be transferred into internal energy. It's all about the efficiency of this transfer: If you have water @ 5°C and you know that it looses $$\Delta U = 50cal$$, if it is cooled down to 0°C, does this mean that you are able to provide $$W=50cal$$ to power a light bulb? Well, probably not, because the process will generate heat $$Q \ne 0$$. Thus, the change in the internal energy $$\Delta U = 50cal$$ will split into two parts: A work part $$W$$, which we can use to power the light bulb and a heat part $$Q$$ which will be "lost" in the context of "using it for the light bulb". Thus, the law of energy conservation is maintained, although we are unable to transfer all the internal energy into work.

• (1) Thank you for your answer. I had to re-read it several times, but i still I couldn’t understand some points. Perhaps, I need a kind of simple illustration here. “Heat is a quantity, which we do not (!) store in a system” – What does “store in a system” mean in the first place? Dec 22, 2019 at 10:30
• (2) If I take a crowbar and transfer a whole lot of heat into it by means of holding its end out over a fire to the point when it starts glowing red, you may still say that it doesn’t store in its system the heat that has been transferred into it, but I will still not dare touch it because I know that now it contains a lot more heat that it contained before. What’s the difference between “stores in its system” and “contains”? Dec 22, 2019 at 10:30
• (3) “we know that water at 5°C contains a certain amount of energy. However, this energy is not stored as "heat", but as so called internal energy” – So if it’s the internal energy, then what will happen to it if I cool that water down to +1°C? Will that mean that some part of its internal energy be gone now? If yes, that is, the internal energy can be turned into transferred energy, then why transferred energy cannot be transferred into internal one? Dec 22, 2019 at 10:38
• You can think of the term 'heat' as a credit card. Is money(energy) stored as the credit card? No, the credit card is just there when there is a transfer of some money. It is transferred in the bank account(internal energy). When this bank account comes in contact with another relatively poorer bank account, there is a transfer of some money(energy). and again, only while this transfer from the richer to the poorer is happening, a credit card, or some technology is used. The credit card is like the term 'heat'. Note that I'm trying to relate a physical object to a term in english. Dec 22, 2019 at 10:53
• The physical object is the credit card and the term in english is 'heat' Dec 22, 2019 at 10:54