Q. No.If minimum possible work is done by a refrigerator in converting \(100\) grams of water at \(0^\circ \mathrm{C}\) to ice, how much heat (in calories) is released to the surroundings at temperature \(27^\circ \mathrm{C}\) (Latent heat of ice = \(80\) cal/gram) to the nearest integer?
1. \(3242\)
2. \(8791\)
3. \(1634\)
4. \(100\)
1. \(3242\)
2. \(8791\)
3. \(1634\)
4. \(100\)
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:
| 1. | \(E_{A B}=E_{A C}=E_{A D}, W_{A B}>0, W_{A C}=0, W_{A D}<0\) |
| 2. | \(E_{A B}<E_{A C}<E_{A D}, W_{A B}>0, W_{A C}>W_{A D}\) |
| 3. | \(E_{A B}=E_{A C}<E_{A D},W_{A B}>0,W_{A C}=0, W_{A D}<0\) |
| 4. | \(E_{A B}>E_{A C}>E_{A D}, \quad W_{A B}< W_{A C}< W_{A D}\) |
In an adiabatic process, the density of a diatomic gas becomes \(32\) times its initial value. The final pressure of the gas is found to be \(n\) times the initial pressure. The value of \(n\) is:
1. \(326\)
2. \(\dfrac{1}{32}\)
3. \(32\)
4. \(128\)
A closed vessel contains \(0.1\) mole of a monatomic ideal gas at \(200\) K. If \(0.05\) mole of the same gas at \(400\) K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be closed to:
1. \(133\)
2. \(57\)
3. \(266\)
4. \(504\)
\(n\) moles of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.
| \(A\rightarrow B\) | Isothermal expansion at temperature \(T\) so that the volume is doubled from \(V_1\) to \(V_2=2V_1\) and pressure changes from \(P_1\) to \(P_2.\) |
| \(B\rightarrow C\) | Isobaric compression at pressure \(P_2\) to initial volume \(V_1\). |
| \(C\rightarrow A\) | Isochoric change leading to change of pressure from \(P_2\) to \(P_1\). |
Total work done in the complete cycle \(ABCA\) is:
1. \(0\)
2. \(nRT(\ln 2-\frac{1}{2})\)
3. \(nRT\ln 2\)
4. \(nRT(\ln 2+\frac{1}{2})\)
Match List-I with List-II and choose the correct option:
| List-I | List-II | ||
| (a) | Isothermal process | (i) | Pressure constant |
| (b) | Isochoric process | (ii) | Temperature constant |
| (c) | Adiabatic process | (iii) | Volume constant |
| (d) | Isobaric process | (iv) | Heat content is constant |
| 1. | (a) → (i), (b) → (iii), (c) → (ii), (d) → (iv) |
| 2. | (a) → (ii), (b) → (iii), (c) → (iv), (d) → (i) |
| 3. | (a) → (ii), (b) → (iv), (c) → (iii), (d) → (i) |
| 4. | (a) → (iii), (b) → (ii), (c) → (i), (d) → (iv) |
The thermodynamic process is shown below on a \(P-V\) diagram for one mole of an ideal gas. If \(V_2=2V_1\) then the ratio of temperature \(T_2/T_1\) is:
1. \(\frac{1}{2}\)
2. \(2\)
3. \(\sqrt{2}\)
4. \(\frac{1}{\sqrt{2}}\)
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 work done by the gas is:
1. \(RT\left(\ln 2-\dfrac{1}{2(\gamma-1)}\right) \)
2. \(-\dfrac{RT}{2(\gamma-1)} \)
3. \(0\)
4. \(RT\ln2\)
A diatomic gas, having \(C_P=\dfrac{7}{2}R\) and \(C_V=\dfrac{5}{2}R\) is heated at constant pressure. The ratio of \(dU:dQ:dW\) is:
1. \(5:7:3\)
2. \(5:7:2\)
3. \(3:7:2\)
4. \(3:5:2\)
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)
| 1. | \(20nR\) | 2. | \(30nR\) |
| 3. | \(40nR\) | 4. | \(50nR\) |
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