Ideal Gas Questions

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

Two chambers $(V_1,P_1,T_1)$ and $(V_2,P_2,T_2)$ are separated by an insulating partition. If the partition is removed, the final equilibrium temperature is:

One kg of a diatomic gas is at a pressure of $8\times 10^4{\text{N/m}}^2$. The density of the gas is $4{\text{kg/m}}^3$. What is the energy of the gas due to its thermal motion?

Directions: Question numbers 28, 29 and 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the P – T diagram.

Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P–T$ diagram. Assuming the gas to be ideal, the work done on the gas in taking it from $A$ to $B$ is:

Three perfect gases at absolute temperatures $T_1,T_2$ and $T_3$ are mixed. The masses of molecules are $m_1,m_2$ and $m_3$ and the number of molecules are $n_1,n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is: