Question

Two vessels of volumes V₁ and V₂ contain the same ideal gas. The pressures in the vessels are P₁ and P₂ the temperatures are T₁ and T₂ respectively. The two vessels are now connected to each other through a narrow tube. Assuming that no heat is exchange between the surrounding and the vessels, find the common pressure and temperature attained after the connection. 

Answer 1

In order to find out the common pressure and temperature attained after the connection, first we have to find out what is the amount of gas present in vessel one and two the formula to be used is

 The amount if the gas in vessel 1 is

n₁ = p₁V₁/RT₁ and that in vessel 2 is n₂ = P₂V₂/RT₂

If p’ and T’ be the common pressure and temperature after the connection is made, the amounts are

As the vessels have fixed volume, no work is done by the gas plus the vessels system. Also no heat is exchanged with the surrounding. Thus, the internal energy if the total system remains constant. 

The internal energy of an ideal gas is 

The internal energy of the gases before the connection

And after the connection

Neglecting the change in internal energy of the vessels (the heat capacity of the vessels is assumed negligible),