Which of the following relations does not give the equation of an adiabatic process, where terms have their usual meaning? 
1. \(\mathrm{P}^{1-\gamma} \mathrm{T}^\gamma= \text{constant}\)
2. \(\mathrm{PV}^\gamma=\text{ constant }\)
3. \(\mathrm{TV}^{\gamma-1}= \text{constant }\)
4. \(\mathrm{P}^{\gamma} \mathrm{T}^{1-\gamma}= \text{constant}\)

A monoatomic gas at pressure P₁ and volume V₁ is compressed adiabatically to 1/8th its original volume. What is the final pressure of the gas?

1. P₁

2. 16 P₁

3. 32 P₁

4. 64 P₁

At a pressure of \(2\) atmospheres, a mass of diatomic gas \((\gamma = 1.4)\), is compressed adiabatically, causing its temperature to rise from \(27^{\circ}\mathrm{C}\) to \(927^{\circ}\mathrm{C}\). The pressure of the gas in the final state is:
1. 8 atm
2. 28 atm
3. 68.7 atm
4. 256 atm

An ideal gas goes from state \(A\) to state \(B\) via three different processes as indicated in the \((P\text-V)\) diagram.

  
If \(Q_1,Q_2,Q_3\)${\mathrm{}}_{}$ indicate the heat absorbed by the gas along the three processes and \(\Delta U_1, \Delta U_2, \Delta U_3\) indicate the change in internal energy along the three processes respectively, then:

The molar specific heat at a constant pressure of an ideal gas is \(\frac{7}{2}R.\) The ratio of specific heat at constant pressure to that at constant volume is:
1. \(\frac{7}{5}\)
2. \(\frac{8}{7}\)
3. \(\frac{5}{7}\)
4. \(\frac{9}{7}\)

A Carnot engine whose sink is at \(300~\mathrm{K}\) has an efficiency of \(40\)%. By how much should the temperature of the source be increased to increase its efficiency by \(50\)% of its original efficiency?

If \(Q\), \(E\), and \(W\) denote respectively the heat added, the change in internal energy, and the work done in a closed cycle process, then:
1. \(W=0\)
2. \(Q=W=0\)
3. \(E=0\)
4. \(Q=0\)

In thermodynamic processes which of the following statements is not true?

The internal energy change in a system that has absorbed \(2\) kcal of heat and done \(500\) J of work is:
1. \(8900\) J
2. \(6400\) J
3. \(5400\) J
4. \(7900\) J