This question makes no sense to me. The heat capacity is supposed to be a physical property of the material, independent of any process that the material is subjected to.Krushnaraj Pandya said:Homework Statement
In a certain process, a gas absorbs Q amount of heat and performs kQ amount of work, the molar heat capacity of the gas in terms of R, k and γ(Cp/Cv) is?
Homework Equations
U=Q+W
U=nCvdT
Q=CdT
The Attempt at a Solution
replacing U and Q with the above formulas and W from the given information gives C = (CvdT + kQ)/dT How do I proceed further?
well, I saw a formula that for a polytropic process with index n, the heat capacity is C=Cv + R/1-x.Chestermiller said:This question makes no sense to me. The heat capacity is supposed to be a physical property of the material, independent of any process that the material is subjected to.
Was this the exact statement (word for word) of the problem? What book did this problem come from?
Wait they taught/are teaching me the same thing in school too !Chestermiller said:Well, I can help you solve this problem but, with the following caveat: I think it is a very bad idea to define heat capacity in terms of the temperature change and heat added for a specified process path. The heat capacity is supposed to be a physical property of the material being processed, independent of process path. Defining it in terms of heat (process path) causes nothing but confusion for thermodynamics students later on. For example, when the student studies adiabatic expansions and compressions of gases, the heat Q is zero, but there is a temperature change. So the student calculates that the heat capacity of the gas is zero. Instant confusion! With this warning, I will now help you solve this.
I hate to bust your balloon, but that's not the way we do it in thermodynamics. In thermodynamics, we define heat capacity as a physical property of the material, in terms of the equilibrium thermodynamic functions U and H:Navin said:Wait they taught/are teaching me the same thing in school too !
And we defined Heat capacity in terms of the process the gas undergoes and we also defined that Cad(heat capacity of gas for adiabetic process) is Zero !
Dont tell me all that is wrong !
And in the JEE Advance/NEET/AIIMS Prepetory module my school provided me with we have tonnes of questions,all talking about heat capacity in terms of the process it undergoes !
Is my life a lie ?,
...*sigh*Chestermiller said:I hate to bust your balloon, but that's not the way we do it in thermodynamics. In thermodynamics, we define heat capacity as a physical property of the material, in terms of the equilibrium thermodynamic functions U and H:
$$C_v=\left(\frac{\partial U}{\partial T}\right)_V\tag{1}$$
$$C_p=\left(\frac{\partial H}{\partial T}\right)_P\tag{2}$$
These definitions reduce to the old definition in terms of heat only for a process at constant volume or a process at constant pressure. If we don't adopt these new definitions, it leads to great confusion and ambiguity.
That being said, you still need to pass your course. So you need to "play the game" the way they expect you to play play the game. Just bear in mind that it is not the correct way to do it in thermodynamics. They have basically done you a disservice by teaching it to you in this way. One very good thermodynamics book is Fundamentals of Engineering Thermodynamics by Moran et al; here, when they introduce heat capacity, they go immediately to the definition given by Eqns. 1 and 2.
same here. which coaching?Navin said:And in the JEE Advance/NEET/AIIMS Prepetory module my school provided me with we have tonnes of questions,all talking about heat capacity in terms of the process it undergoes !
I solved it, thank you very much :DChestermiller said:Well, I can help you solve this problem but, with the following caveat: I think it is a very bad idea to define heat capacity in terms of the temperature change and heat added for a specified process path. The heat capacity is supposed to be a physical property of the material being processed, independent of process path. Defining it in terms of heat (process path) causes nothing but confusion for thermodynamics students later on. For example, when the student studies adiabatic expansions and compressions of gases, the heat Q is zero, but there is a temperature change. So the student calculates that the heat capacity of the gas is zero. Instant confusion! With this warning, I will now help you solve this.
You indicated that the change in internal energy is given by $$\Delta U=C_v\Delta T=Q-W$$where W is the work done by the gas on its surroundings. If you substitute W from the problem statement into this equation, what do you get for the temperature change ##\Delta T##?
I wouldn't like to tell the name because a loooot of my classmates use this site and in the state i live in there are only 3 good coaching institutes so i will be easily identified by them , and i wouldn't like that to happen ! I wouldn't mind PM-ing you the name though if you wantKrushnaraj Pandya said:same here. which coaching?
R/(γ-1)(1-k)Navin said:Oh and what's the answer you have got ?
Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius.
The heat capacity of a gas is calculated by dividing the amount of heat energy absorbed by the gas by the change in temperature.
Specific heat capacity is the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius. Molar heat capacity is the amount of heat energy required to raise the temperature of one mole of a substance by one degree Celsius. Essentially, specific heat capacity is per unit mass and molar heat capacity is per unit amount of substance.
The heat capacity of a gas typically increases with temperature. However, the rate of increase may vary depending on the type of gas and its molecular structure.
Gases generally have a higher heat capacity than solids and liquids. This is because gases have more freedom of movement, allowing them to absorb more heat energy without a significant increase in temperature. Solids and liquids, on the other hand, have a more fixed structure which limits their ability to absorb heat energy.