An ideal gas is pumped into a rigid container having a diathermic wall so that the temperature remains constant. In a certain time interval, the pressure in the container is doubled. Is the internal energy of the contents of the container also doubled in the interval?
Yes, the internal energy will also be doubled.
Explanation
1. Internal energy for an ideal gas is given as
U=nCvT
Where U= internal energy
N=number of moles
Cv=molar specific heat at constant volume
T= temperature
2. Since the ideal gas is continuously pumped into rigid container number of moles are also increasing.
3. When the pressure becomes doubled, the number of moles also gets doubled.
4. It is given that the temperature remains constant. So internal energy depends only on the number of moles.
5. Internal energy will also be doubled as the number of moles is getting doubled.