CSIR (Council of Scientific & Industrial Research) Physical Sciences: Questions 1 of 463
» Thermodynamic and Statistical Physics » Thermodynamic Potentials
Appeared in Year: 2013
Question
A vessel has two compartments of volume V_{1} and V_{2}, containing an ideal gas at pressure P_{1} and P_{2}, and temperatures T_{1} and T_{2} respectively. If the wall separating the compartments is removed, the resultant equilibrium temperature will be – (June)
Choices
Choice (4)  Response  

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Answer
Explanation
Here, volume of the vessel does not changed, therefore no work done by the surrounding on the gas; because no heat transferred from surrounding to system. Therefore total internal energy does not change. So we can consider total internal energy of the vessel is sum of two internal energies in the two compartments.
Now, if the gas have ideal gas characteristic than internal energies are given as,
Where, T is the equilibrium temperature, are the numbers of moles of gasses, which are in different compartment.
From equation (1),
Now for ideal gas,
From equation (2),