The initial pressure and volume of a gas are \(P\) and \(V\), respectively. First, it is expanded isothermally to volume \(4V\) and then compressed adiabatically to volume \(V\). The final pressure of the gas will be: [Given: \(\gamma = 1.5\)]

1.	\(P\)	2.	\(2P\)
3.	\(4P\)	4.	\(8P\)

A monoatomic ideal gas, initially at temperature \(T_1\), is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \(T_2\) by releasing the piston suddenly. If \(L_1\) and \(L_2\) are the lengths of the gas column before and after expansion, respectively, then \(\frac{T_1}{T_2}\) is given by:
1. \(\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}\)
2. \(\frac{L_1}{L_2}\)
3. \(\frac{L_2}{L_1}\)
4. \(\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}\)

Calculate the Gibbs energy change when 1 mole of NaCl is dissolved in water at 298 K. Given,

a. Lattice energy of NaCl = 778 kJ mol^-1

b. Hydration energy of NaCl =-774.3 kJ mol^-1

c. Entropy change at 298 K = 43 JK^-1 mol^-1

Work done during the given cycle is:
                               
1. 4$P_0{V}_0$

2. 2$P_0{V}_0$

3. $\frac{1}{2}$$P_0{V}_0$

4. $P_0{V}_0$

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:

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:

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. \(2 \mathrm{NH}_3 (g) ~\rightarrow ~\mathrm{N}_2(g)+3 \mathrm{H}_2(g)\)

1 kg of gas does 20 kJ of work and receives 16 kJ of heat when it is expanded between two states. The second kind of expansion can be found between the same initial and final states, which requires a heat input of 9 kJ. The work done by the gas in the second expansion will be:

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)