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1.

A cylinder with a movable piston contains \(3\) moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

1.	\(3.70\)	2.	\(2.12\)
3.	\(2.64\)	4.	\(3.33\)

2. Two cylinders, \(A\) and \(B,\) of equal capacity are connected to each other via a stopcock. \(A\) contains gas at a standard temperature and pressure \(B\) is completely evacuated. The entire system is thermally insulated. If the stopcock is suddenly opened, then the change in internal energy of the gas is:
1. \(0\)
2. \(5~\text{J}\)
3. \(1~\text{J}\)
4. \(3~\text{J}\)

3.

A thermodynamic system is taken from an original state to an intermediate state by the linear process shown in the figure. Its volume is then reduced to the original value from \(E\) to \(F\) by an isobaric process. The total work done by the gas from \(D\) to \(E\) to \(F\) is:

1. \(600 ~\text{J}\)
2. \(300 ~\text{J}\)
3. \(450 ~\text{J}\)
4. \(500 ~\text{J}\)

4.

An ideal gas undergoes four different processes from the same initial state (figure). Four processes are adiabatic, isothermal, isobaric and isochoric. Out of \(1,\) \(2,\) \(3\) and \(4,\) which one is adiabatic?
 

1.	\(4\)	2.	\(3\)
3.	\(2\)	4.	\(1\)

5.

Consider the \((P\text-V)\) diagram for an ideal gas shown in the figure.

Out of the following diagrams, which figure represents the \((T\text-P)\) diagram?

1.		2.
3.		4.

6. Consider two containers A and B containing identical gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original value adiabatically. The ratio of final pressure of gas in B to that of gas in A is
1. \(2^{\gamma-1} \)
2. \(\left(\frac{1}{2}\right)^{\gamma-1} \)
3. \(\left(\frac{1}{1-\gamma}\right)^2 \)
4. \(\left(\frac{1}{\gamma-1}\right)^2\)

7.

The figure shows the \((P\text-V)\) diagram of an ideal gas undergoing a change of state from \(A\) to \(B.\) Four different paths \(\mathrm{I, II, III}\) and \(\mathrm{IV},\) as shown in the figure, may lead to the same change of state.
               

(a)	The change in internal energy is the same in cases \(\mathrm{IV}\) and \(\mathrm{III}\) but not in cases \(\mathrm{I}\) and \(\mathrm{II}.\)
(b)	The change in internal energy is the same in all four cases.
(c)	The work done is maximum in case \(\mathrm{I}.\)
(d)	The work done is minimum in case \(\mathrm{II}.\)

Which of the following options contains only correct statements?

1.	(b), (c) and (d) only	2.	(a) and (d) only
3.	(b) and (c) only	4.	(a), (c) and (d) only

8.

Consider a cycle followed by an engine (figure). 

1 to 2 is isothermal,
2 to 3 is adiabatic,
3 to 1 is adiabatic.
Such a process does not exist, because:

(a)	heat is completely converted to mechanical energy in such a process, which is not possible.
(b)	In this process, mechanical energy is completely converted to heat, which is not possible.
(c)	curves representing two adiabatic processes don’t intersect.
(d)	curves representing an adiabatic process and an isothermal process don't intersect.

Choose the correct alternatives:

1.	(a), (b)	2.	(a), (c)
3.	(b), (c)	4.	(c), (d)

9. An ideal gas undergoes a cyclic process \(ABCDA\) as shown in given \(P\text-V\) diagram given below. The amount of work done by the gas is:
           
1. \(6 P_0 V_0\)
2. \(-2 P_0 V_0 \)
3. \(+2 P_0 V_0 \)
4. \(+4 P_0 V_0\)