\(n\) 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. \(nRT(\ln 2+\frac{1}{2})\)

Subtopic:  Work Done by a Gas |
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The same amount of heat is supplied to equimolar masses of hydrogen and helium, under constant pressure. The work done by the two gases, \(H_2\) and \(He,\) are \(W_1\) and \(W_2.\) Then:
1. \(W_1>W_2\)
2. \(W_1<W_2\)
3. \(W_1=W_2\)
4. \(W_1\) and \(W_2\) cannot be compared unless the temperatures are known.
Subtopic:  Work Done by a Gas |
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Two monoatomic gases \(A,B\) are taken in two parts of a vessel having equal volumes \(V_0.\) The gases are at the same pressure \(P_0\) but at temperature of \(300~\text K\) and \(600~\text K.\) There is a partition between the parts of the vessel. The partition is removed, and the gases are allowed to mix. The vessel, as a whole, is insulated. The final temperature of the system is:

1. \(450~\text K\)
2. \(400~\text K\)
3. \(500~\text K\)
4. \(550~\text K\)
Subtopic:  Work Done by a Gas |
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An ideal monoatomic gas undergoes a reversible process in which it doubles in volume, the equation of the process being:    \(pVT=\text{constant}.\)
The internal energy of the gas at the beginning of the process equals \(U_0.\) The work done by the gas equals:
1. \(U_0\) 2. \({\Large\frac23}U_0\)
3. \(U_0\mathrm{ln}2\) 4. \({\Large\frac23}U_0\mathrm{ln}2\)
Subtopic:  Work Done by a Gas |
 55%
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One mole of an ideal monoatomic gas undergoes a slow reversible process in which its density \((\rho)\) is inversely proportional to its absolute temperature \((T).\)
The temperature of the gas increases from \(300~\text K\) to \(400~\text K.\) The work done by the gas during the process is:
(\(R\text:\) universal gas constant)
1. zero
2. \(-100~R\)
3. \(100~R\)
4. \(50~R\)
Subtopic:  Work Done by a Gas |
 59%
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