# Heat Capacity of Air at Constant Volume

by s.p.q.r
Tags: capacity, constant, heat, volume
 P: 25 Hi I have an ongoing dispute with my mate on this one, please help to clarify this before I open up a can of whoop *** on that sorry mo-fo. 300 litres of air are compressed into a 3 litre tank. What is the heat capacity of this air? Thanks in advance.
 Emeritus Sci Advisor PF Gold P: 9,789 What do you think it is?
 P: 25 The Cp J mol is 29.19. But because I ask for constant volume, it is definately lower then this. This is what I think. I can find no references to constant volume anywhere and unfortunately I have no teacher to ask as I study archaeology, not physics. Do you have the answer? Thanks in advance.
HW Helper
P: 6,505

## Heat Capacity of Air at Constant Volume

 Quote by s.p.q.r The Cp J mol is 29.19. But because I ask for constant volume, it is definately lower then this. This is what I think. I can find no references to constant volume anywhere and unfortunately I have no teacher to ask as I study archaeology, not physics. Do you have the answer? Thanks in advance.
Air is almost entirely a diatomic gas, $\gamma = C_p/C_v = 1.4$ (7/5)

AM
 P: 25 Hi, Thanks for the reply. Is 1.4 per gram or mol? Also, How can you measure a gram of gas and how much is 1 mol? Cheers.
 Sci Advisor HW Helper P: 8,961 1.4 is a ratio ( actually nearer 1.3 for dry air at room temp) see http://en.wikipedia.org/wiki/Heat_capacity_ratio 1 mol of air is roughly 30g or 22.4litres at STP ( 0deg C 1 atm)
 P: 3,408 Is heat capacity independent of volume for an ideal gas? Stupid question - gas performs work while being compressed.
 Sci Advisor HW Helper P: 8,961 For an ideal gas heat capcity just depends on the amount (number of moles) present and the number of vibration states of the molecular. For a real gas it also depends on the pressure because the molecules close to each other change the vibration state/bond energy.
 P: 3,408 In a modification of the "ideal gas" law, I seem to recall an equation with correction terms for the volume and pressure, respectively. Has anyone run across this?
 P: 25 Hi, This ratio of 1.4, does this just mean that you divide the constant pressure capacity (1.020J/g) by 1.4?
$\gamma = 1.4$ is the ratio of the specific heat (heat flow per gram or per mole per degree K change in temperature) at constant pressure to the specific heat at constant volume. $\gamma = C_p/C_v$. What you want to find is Cv. You also have to find the number of moles of air in this container to find its heat capacity (heat flow per degree K change in Temp.).