\(n\) moles of an ideal gas with constant volume heat capacity \(C_V\) undergo an isobaric expansion by a certain volume. The ratio of the work done in the process, to the heat supplied is:
1. \( \dfrac{n R}{C_V+n R} \)

2. \( \dfrac{n R}{C_V-n R} \)

3. \( \dfrac{4 n R}{C_V+n R} \)

4. \( \dfrac{4 n R}{C_V-n R}\) 

A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180~\text{J}\). The gas absorbs \(250~\text{J}\) of heat along the path \(ab\) and \(60~\text{J}\) along the path \(bc\). The work done by the gas along the path \(abc\) is:

1. \(140~\text{J}\)
2. \(130~\text{J}\)
3. \(100~\text{J}\)
4. \(120~\text{J}\)

Three different processes that can occur in an ideal monoatomic gas are shown in the \(P\) vs \(V\) diagram. The paths are labelled as \(A \rightarrow B, A \rightarrow C\) and \(A\rightarrow D\). The change in internal energies during these process are taken as \(E_{AB}\), \(E_{AC}\)  and \(E_{AD}\) and the work done as \(W_{A B}, W_{A C}\) and \( W_{A D}\). The correct relation between these parameters are:

\(n\) moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.

Total work done in the complete cycle \(ABCA\) is: 

1. \(0\)
2. \(nRT(\ln 2-\frac{1}{2})\)
3. \(nRT\ln 2\)
4. \(nRT(\ln 2+\frac{1}{2})\)

If one mole of an ideal gas at (\(P_1,V_1 \)) is allowed to expand reversibly and isothermally (\(A\rightarrow B\)) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (\(B\rightarrow C\)). Then it is restored to its initial state by a reversible adiabatic compression (\(C\rightarrow A\)). The net workdone by the gas is equal to:

  
1. \(\operatorname{RT}\left(\ln 2-\frac{1}{(\gamma-1)}\right) \)
2. \(-\frac{\mathrm{RT}}{2(\gamma-1)}\)
3. \(0\)
4. \(RT\ln2\)

In a certain thermodynamical process, the pressure of a gas depends on its volume as \(kV^3.\) The work done when the temperature changes from \(100^\circ \text{C}\) to \(300^\circ \text{C}\) will be:
(where \(n\) denotes number of moles of a gas)

The volume \(V\) of a given mass of monoatomic gas changes with temperature \(T\) according to the relation \(\mathrm{V}=\mathrm{K} \mathrm{T}^{2 / 3}\). The work done when temperature changes by \(90\) K will be:
1. \(60R\)
2. \(30R\)
3. \(20R\)
4. \(10R\)