## Molar Heat Capacity

Matthew Casillas 1C
Posts: 29
Joined: Fri Sep 28, 2018 12:21 am

### Molar Heat Capacity

Why is the molar heat capacity, with constant pressure, equal to the molar heat capacity with constant volume (Cv,m) plus the gas constant (R)?

klarratt2
Posts: 60
Joined: Fri Sep 28, 2018 12:16 am

### Re: Molar Heat Capacity

Heat Capacity at CONSTANT VOLUME
Q = nCVΔT

For an ideal gas, applying the First Law of Thermodynamics tells us that heat is also equal to:
Q = (3/2)nRΔT + W, although W = 0 at constant volume. So, Q = (3/2)nRΔT.

Comparing our two equations
Q = nCVΔT and Q = (3/2)nRΔT

we see that, for a monatomic ideal gas:
CV = (3/2)R

Heat Capacity at CONSTANT PRESSURE
Q = nCPΔT

For an ideal gas, applying the First Law of Thermodynamics tells us that heat is also equal to:
Q = (3/2)nRΔT + W

At constant pressure W = PΔV = nRΔT
Q = (3/2)nRΔT + nRΔT = (5/2)nRΔT

So, for a monatomic ideal gas:
CP = (5/2)R

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