Heat Capacity at Constant Volume
The heat needed to raise a system's temperature by one kelvin while its volume is held fixed.
Formula / equation
C_V = (∂U/∂T)_V
Unit
J/(mol·K)
In depth
At constant volume no expansion work is possible, so every joule supplied raises the internal energy directly. This makes C_V the quantity that appears in kinetic theory, where it equals (3/2)R for a monatomic ideal gas and larger values for molecules with rotational and vibrational modes.
Examples in the real world
Argon has C_V = 12.5 J/(mol·K); nitrogen has 20.8 because it can also rotate.