Find out the total heat given to diatomic gas in the process \(A\rightarrow B \rightarrow C\): \(( B\rightarrow C\) is isothermal)
                 
1. \(P_0V_0+ 2P_0V_0\ln 2\)
2. \(\frac{1}{2}P_0V_0+ 2P_0V_0\ln 2\)
3. \(\frac{5}{2}P_0V_0+ 2P_0V_0\ln 2\)
4. \(3P_0V_0+ 2P_0V_0\ln 2\)

The standard enthalpies of the formation of  NO₂(g) and N₂O₄(g) are 8 kcal mol^–1 and 2 kcal mol^–1 respectively. The heat of dimerization of NO₂ in the gaseous state is: 

\(0.04\) mole of an ideal monatomic gas is allowed to expand adiabatically so that its temperature changes from \(800~\text{K}\) to \(500~\text{K}.\) The work done during expansion is nearly equal to:

             
1. \(V_1= V_2\)
2. \(V_1> V_2\)
3. \(V_1< V_2\)
4. \(V_1\ge V_2\)

A system that can neither exchange matter nor energy with the surroundings is classified as:

1. Open system

2. Isolated system

3. Closed system

4. Both (1) & (2)

Which of the following reactions has the least difference between the change in enthalpy (∆H) and the change in internal energy (∆E) at a given temperature?

1. \(2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_3(\mathrm{~g})\)
2. \(\mathrm{CaCO}_3(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_2(g)\)
3. \(\mathrm{NH}_4 \mathrm{SH} (s) ~~\rightarrow ~\mathrm{NH}_3(g)+\mathrm{H}_2 \mathrm{~S}(g)\)
4. \(2 \mathrm{NH}_3 (g) ~\rightarrow ~\mathrm{N}_2(g)+3 \mathrm{H}_2(g)\)

The pressure-temperature \((P\text-T)\) graph for two processes, \(A\) and \(B,\) in a system is shown in the figure. If \(W_1\) and \(W_2\)${\mathrm{}}_{}$ are work done by the gas in process \(A\) and \(B\) respectively, then:

An ideal gas goes from \(A\) to \(B\) via two processes, \(\mathrm{I}\) and \(\mathrm{II},\) as shown. If \(\Delta U_1\) and \(\Delta U_2\) are the changes in internal energies in processes \(\mathrm{I}\) and \(\mathrm{II},\) respectively,  (\(P:\) pressure, \(V:\) volume) then: