# Specific heat of an ideal gas

1. Jan 12, 2016

### Monsterboy

1. The problem statement, all variables and given/known data
Does the specific heat of an ideal gas depend on the temperature only or does it depend on molecular weight and structure ? or both ?

2. Relevant equations
PV=mRT , Cp -Cv=R

3. The attempt at a solution
One of my teachers said it depends only on temperature and the other said it depends on molecular weight and structure ,i am not sure who is correct ,is it possible to find out who is correct by using the above equations ?

Cv( $\gamma$ -1) = R

PV=RT

PV/T = R = Cv($\gamma$ -1)

$\gamma$ -1 = PV/TCv

I don't know how to proceed.

2. Jan 12, 2016

### Staff: Mentor

It's both. Sometimes physicists talk about perfect gases, for which heat capacity is considered independent of temperature, and sometimes they refer to such gases as ideal gases. Engineers regard the heat capacity of ideal gases as temperature-dependent because real gases approach this behavior in the limit of low pressures (ideal gas limit). For an engineer, the ideal gas heat capacity varies with temperature exactly as the actual gas heat capacity varies (experimentally) in the limit of low pressures.

Ideal gas heat capacity is affected by structure because polyatomic molecules are capable of exhibiting vibrational and rotational energy accumulation.

3. Jan 12, 2016

### Monsterboy

Ok , is it possible to know which factor affects the specific heat more ? is it possible to ignore any of them in engineering point of view ?
Actually for the question i have ,there are four options
A . Temperature B. Is not affected by either
C.Volume D. Molecular weight and structure.

so the answer is A and D ? but this option is not given

4. Jan 12, 2016

### Staff: Mentor

Typically, structure more than temperature.
Often, the temperature dependence can be ignored (over limited ranges of temperature).
Yes, the answer is A and D. But, if this is being taught by Physicists, they may not count A.

5. Jan 12, 2016

### Monsterboy

In an ideal gas, molecules are considered as point masses without any dimensions right ? so how is structure considered as a factor here ?

6. Jan 13, 2016

### ehild

Ideal gas is assumed to consist of non-interacting particles of negligible size with respect to the size of the container. Still, they have structure, moment of inertia, so they have rotational energy in addition to the translational kinetic energy. That is why at about room temperature, Cv of the two-atomic gases is 5/2 R and 3R if the molecules consist of three or more atoms. The molecules also vibrate, and the vibration modes become excited at higher temperatures, making Cv increasing with the temperature.