Question

Starting from the relationship between temperature and kinetic energy for an ideal gas, find the value of the molar heat capacity of an ideal gas when its temperature is changed at constant volume

Answer 1

For an ideal gas, applying the First Law of Thermodynamics tells us that heat is also equal to:

$Q = ΔE_{int} + W$

$W=0$ at constant volume.

For a monatomic ideal gas we showed that

$ΔE_{int} = (3/2)nRΔT$

Comparing our two equations;

$Q = nC_VΔT$ and $Q = (3/2)nRΔT$

we see that, for a monatomic ideal gas:

$C_V = (3/2)R$

For diatomic and polyatomic ideal gases we get:

$diatomic: C_V = (5/2)R$

$polyatomic: C_V = 3R$

So, $C_V=\frac{f}{2}R$