Q. No.A closed hollow insulated cylinder is filled with gas at \(0^{\circ}\mathrm{C}\) and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \(100^{\circ}\mathrm{C}\).
If the piston moves 5 cm, the length of the hollow cylinder will be:
1. 13.65 cm
2. 27.3 cm
3. 38.6 cm
4. 64.6 cm
1. 13.65 cm
2. 27.3 cm
3. 38.6 cm
4. 64.6 cm
A monoatomic gas is supplied with the heat \(Q\) very slowly, keeping the pressure constant. The work done by the gas will be:
1. \({2 \over 3}Q\)
2. \({3 \over 5}Q\)
3. \({2 \over 5}Q\)
4. \({1 \over 5}Q\)
1. \(\dfrac{2}{5}R\)
2. \(\dfrac{5}{2}R\)
3. \(\dfrac{10}{3}R\)
4. \(\dfrac{6}{7}R\)
A cyclic process for \(1\) mole of an ideal gas is shown in the \(V\text-T\) diagram. The work done in \(AB, BC\) and \(CA\) respectively is:
| 1. | \(0, R T_2 \ln \left(\frac{V_1}{V_2}\right), R\left(T_1-T_2\right)\) |
| 2. | \(R\left(T_1-T_2\right), 0, R T_1 \ln \frac{V_1}{V_2}\) |
| 3. | \(0, R T_2 \ln \left(\frac{V_2}{V_1}\right), R\left(T_1-T_2\right)\) |
| 4. | \(0, R T_2 \ln \left(\frac{V_2}{V_1}\right), R\left(T_2-T_1\right)\) |
The Carnot cycle (reversible) of gas is represented by a pressure-volume curve as shown in the figure. Consider the following statements:
| I. | The area \(ABCD\) = The work done on the gas |
| II. | The area \(ABCD\) = The net heat absorbed |
| III. | The change in the internal energy in the cycle = \(0\) |
Which of the statement(s) given above is/are correct?
| 1. | I only | 2. | II only |
| 3. | II and III | 4. | I, II, and III |
Which one of the following is correct for one complete cycle of a thermodynamic process on a gas as shown in the \((P-V)\) diagram?
| 1. | \(\Delta E_{int}= 0, Q<0\) | 2. | \(\Delta E_{int}= 0, Q>0\) |
| 3. | \(\Delta E_{int}>0, Q<0\) | 4. | \(\Delta E_{int}< 0, Q>0\) |
In the following figures, four curves A, B, C and D, are shown. The curves are:
| 1. | isothermal for A and D while adiabatic for B and C. |
| 2. | adiabatic for A and C while isothermal for B and D. |
| 3. | isothermal for A and B while adiabatic for C and D. |
| 4. | isothermal for A and C while adiabatic for B and D. |
When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is:
| 1. | \(\dfrac{2}{5}\) | 2. | \(\dfrac{3}{5}\) |
| 3. | \(\dfrac{3}{7}\) | 4. | \(\dfrac{5}{7}\) |
In a Carnot engine, when \(T_2=0^\circ \mathrm{C}\) and \(T_1=200^\circ \mathrm{C},\) its efficiency is \(\eta_1\) and when \(T_1=0^\circ \mathrm{C}\) and \(T_2=-200^\circ \mathrm{C},\) its efficiency is \(\eta_2.\) What is the value of \(\frac{\eta_1}{\eta_2}?\)
| 1. | 0.577 | 2. | 0.733 |
| 3. | 0.638 | 4. | cannot be calculated |
In a cyclic process, the internal energy of the gas:
| 1. | increases | 2. | decreases |
| 3. | remains constant | 4. | becomes zero |
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