Q. No.A certain gas is isothermally compressed to\(\left(\dfrac{1}{3}\right)^{\text {rd }}\) of its initial volume \((V_0=3 ~\text{litre})\) by applying required pressure. If the bulk modulus of the gas is\(3 \times 10^5 ~\text{N/m}^2,\) the magnitude of work done on the gas is: (in J)
1. \(750\)
2. \(760\)
3. \(706\)
4. \(989\)
1. \(750\)
2. \(760\)
3. \(706\)
4. \(989\)
Subtopic: Work Done by a Gas |
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The internal energy of a monoatomic gas is \(3nRT\). One mole of helium is kept in a cylinder having internal cross section area of \(17~\text{cm}^2\) and fitted with a light movable frictionless piston. The gas is heated slowly by suppling \(126~\text{J}\) heat. If the temperature rises by \(4^{\circ}\text{C}\), then the piston will move: (in cm)
(atmospheric pressure = \(105~\text{Pa}\))
1. \(14.5\)
2. \(1.55\)
3. \(15.3\)
4. \(1.45\)
(atmospheric pressure = \(105~\text{Pa}\))
1. \(14.5\)
2. \(1.55\)
3. \(15.3\)
4. \(1.45\)
Subtopic: Work Done by a Gas |
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One mole of an ideal diatomic gas expands from volume \(V\) to \(2V\) isothermally at a temperature \(27^{\circ}\text{C}\) and does \(W\) joule of work. If the gas undergoes same magnitude of expansion adiabatically from \(27^{\circ}\text{C}\) doing the same amount of work \(W\), then its final temperature will be: (close to) (in \(^{\circ}\text{C}\))
1. \(-189\)
2. \(-56\)
3. \(-30\)
4. \(-117\)
1. \(-189\)
2. \(-56\)
3. \(-30\)
4. \(-117\)
Subtopic: Work Done by a Gas |
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In the following \(p\text-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4ap\) where \(a\) is a constant. The total work done in the closed path is:
1. \(-\dfrac {1}{a} \)
2. \(+\dfrac {1}{3a}\)
3. \(\dfrac {1}{2a}\)
4. \(-\dfrac {1}{3a}\)
1. \(-\dfrac {1}{a} \)
2. \(+\dfrac {1}{3a}\)
3. \(\dfrac {1}{2a}\)
4. \(-\dfrac {1}{3a}\)
Subtopic: Work Done by a Gas |
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A thermodynamic system is taken through the cyclic process \(ABC\) as shown in the figure. The total work done by the system during the cycle \(ABC\) is: (in J)
1. \(320\)
2. \(300\)
3. \(380\)
4. \(400\)
1. \(320\)
2. \(300\)
3. \(380\)
4. \(400\)
Subtopic: Work Done by a Gas |
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Level 1: 80%+
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An ideal gas exists in a state with pressure \(P_0,\) volume \(V_0.\) It is isothermally expanded to \(4\) times of its initial volume \((V_0),\) then isobarically compressed to its original volume. Finally, the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is:
1. \(P_0 V_0(2 \ln 2-0.75) ~\)
2. \(P_0 V_0( \ln 2-0.75) ~\)
3. \(P_0 V_0(\ln 2-0.25) ~\)
4. \(P_0 V_0(2 \ln 2-0.25) ~\)
1. \(P_0 V_0(2 \ln 2-0.75) ~\)
2. \(P_0 V_0( \ln 2-0.75) ~\)
3. \(P_0 V_0(\ln 2-0.25) ~\)
4. \(P_0 V_0(2 \ln 2-0.25) ~\)
Subtopic: Work Done by a Gas |
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A piston of mass \(M \) is hung from a massless spring whose restoring force law goes as \(F = -kx^3 , \) where \(k\) is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with \(n\) moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature \(T\)) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height \(L_0 \) to \(L_1, \) the total energy delivered by the filament is: (Assume spring to be in its natural length before heating)
| 1. | \(n R T \ln \left(\dfrac{{L}_1}{{L}_0}\right)+{Mg}\left({~L}_1-{L}_0\right)+\dfrac{{k}}{4}\left({~L}_1^4-{L}_0{ }^4\right) ~\) |
| 2. | \(n \mathrm{RT} \ln \left(\dfrac{{~L}_1}{{~L}_0}\right)+{Mg}\left({~L}_1-{L}_0\right)+\dfrac{3{k}}{4}\left({~L}_1{ }^4-{L}_0{ }^4\right) ~\) |
| 3. | \(n R T \ln \left(\dfrac{{~L}_1^2}{{~L}_0^2}\right)+\frac{{Mg}}{2}\left({~L}_1-{L}_0\right)+\dfrac{{k}}{4}\left({~L}_1{ }^4-{L}_0{ }^4\right) ~\) |
| 4. | \(3{nRT} \ln \left(\dfrac{{~L}_1}{{~L}_0}\right)+2 {Mg}\left({~L}_1-{L}_0\right)+\dfrac{{k}}{3}\left({~L}_1{ }^3-{L}_0{ }^3\right) ~\) |
Subtopic: Work Done by a Gas |
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Using the given \(PV\) diagram, the work done by an ideal gas along the path \(ABCD\) is :
1. \(-4P_0V_0\)
2. \(3P_0V_0\)
3. \(-3P_0V_0\)
4. \(4P_0V_0\)
1. \(-4P_0V_0\)
2. \(3P_0V_0\)
3. \(-3P_0V_0\)
4. \(4P_0V_0\)
Subtopic: Work Done by a Gas |
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The work done in an adiabatic change in an ideal gas depends upon only:
| 1. | change in its pressure |
| 2. | change in its temperature |
| 3. | change in its specific heat |
| 4. | change in its volume |
Subtopic: Work Done by a Gas |
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A real gas within a closed chamber at \( 27°\)C undergoes the cyclic process as shown in figure. The gas obeys \(\mathrm{PV}^3=\mathrm{RT}\) equation for the path A to B. The net work done in the completer cycle is (assuming \(R = 8\) J/molK)
1. \(-20\) J
2. \(205\) J
3. \(20\) J
4. \(225\) J
1. \(-20\) J
2. \(205\) J
3. \(20\) J
4. \(225\) J
Subtopic: Work Done by a Gas |
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