Constant Volume Heating
There is no work in constant volume heating.
- Measure δQ and dT, and define
Since there is no work, dU = δQ. The definition of entropy gives δQrev=T dS , and we have
Often, CV= CV(T) (e.g. ideal gas, incompressible substance), or CV=constant. (perfect gas)
EXAMPLE: C V for an Ideal Gas
• In general, for any pure substance, we can write u as a function of two independent properties, such as u = u(T,v) and it follows that
Introducing our definition gives
In general, we must realize that . However, in the case of an ideal gas, we know from Joule’s free expansion experiment that
, so that
du = CvdT
Since u is a function only of temperature for an ideal gas, it follows that CV also must be a function of temperature for an ideal gas:
for an ideal gas.