# Heating gas at constant volume/pressure

1. May 10, 2013

### CAF123

1. The problem statement, all variables and given/known data
A vessel containing 0.33 mol of oxygen gas is allowed to expand at constant pressure while being heated. How much energy is required to raise the temperature of the gas from 300K to 500K?

If the same vessel contains 0.33 mol of argon, calculate the energy required to raise the temperature from 300K to 500K, whilst maintaing the gas at constant volume.

2. Relevant equations
$\Delta E = Q + W$, (First Law of Thermodynamics)

3. The attempt at a solution
At 300K, oxygen exhibits 5 degrees of freedom, so $C_v = \frac{5}{2}R \Rightarrow C_p = \frac{7}{2}R$ At constant pressure, when the gas is being heated up, it must do work and expand (otherwise if it didn't, it's internal energy would increase and thus the pressure on the container). So then $Q = C_p \nu \Delta T$, with $\nu = 0.33, \Delta T = 200$.

Argon is monatomic so $C_v = \frac{3}{2}R.$ At constant volume, the gas does no work so all the heat energy goes into increasing the total internal energy of the gas. This is $Q = C_v \nu \Delta T$ with the same numbers used above.

Is it correct?

Many thanks.

2. May 10, 2013

### TSny

Looks good to me.