1. For the given cycle, the work done during isobaric process is:

(1).200 J

(2). Zero

(3). 400 J

(4). 600 J

2. A container of volume \(200\, cm^3\) contains 0.2 mole of hydrogen gasand 0.3 mole of argon gas. The pressure of the system at temperature 200 K ( \(R=8.3\,JK^{−1} mol^{−1}\)) will be

(1).\(6.15 X 10^5\, pa\)

(2). \(6.15 X 10^4\, pa\)

(3). \(4.15 X 10^5\, pa\)

(4). \(4.15 X 10^6\, pa\)

3. The temperature of a gas is \(−50^\circ C\). To what temperature the gas should be heated so that the rms speed is increased by 3 times?

(1).\(3295^\circ C\)

(2). \(3097\,K\)

(3). \(223\,K\)

(4). \(669^\circ C\)

4. A Carnot engine has an efficiency of 50% when its source is at a temperature \(327^\circ C\). The temperature of the sink is

(1).\(15^\circ C\)

(2). \(100^\circ C\)

(3). \(200^\circ C\)

(4). \(27^\circ C\)

5. An ideal gas follow a process described by the equation \(PV^2 = C \) from the initial (\(P_1\), \(V_1\), \(T_1\)) to final (\(P_2\), \(V_2\), \(T_2\)) thermodynamic states, where C id a constant. Then

(1).If \(P_1\, >\, P_2\) then \(V_1\, >\, V_2\)

(2). If \(P_1\, >\, P_2\) then \(T_1\, <\, T_2\)

(3). If \(V_2\, >\, V_1\) then \(T_2\, >\, T_1\)

(4). If \(V_2\, >\, V_1\) then \(T_2\, <\, T_1\)

6. Two rods one made of copper and other made of steel of same length and same cross-sectional area are joined together. The thermal conductivity of copper and steel are \(385\, J s^{−1} K^{−1} m^{−1}\) and \(50\, Js^{−1} K^{−1} m^{−1}\) respectively. The free ends of copper and steel are held at \(100^\circ C\) and \(0^\circ C\) respectively. The temperature at the junction is, nearly:

(1).\(88.5^\circ C\)

(2). \(12^\circ C\)

(3). \(50^\circ C\)

(4). \(73^\circ C\)

7. Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is :

(1).The root mean square of sulfur hexafluoride is the largest

(2). All vessels contain number of respective molecules

(3). The root mean square speed of molecules is same in all three cases

(4). The root mean suare speed of helium is the largest

8. An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is

(1).1

(2). 2

(3). 3

(4). 4

9. The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is

(1).\(5.6 x 10^6\, m^3\)

(2). \(5.6 x 10^3\, m^3\)

(3). \(5.6 x 10^{-3}\, m^3\)

(4). \(5.6\,m^3\)

10. 1g of water, of volume \(1\,cm^3\) at 100°C is converted into steam at same temperature under normal atmospheric pressure = (~\(1 × 10^5\,Pa\)). The volume of steam formed equals \(1671\,cm^3\) . If the specific latent heat of vaporisation of water is \(2256\, J/g\), the change in internal energy is

(1).2423 J

(2). 2089 J

(3). 167 J

(4). 2256 J

11. A sample of 0.1 g of water at 100°C and normal pressure (\(1.013 X 10^5 Nm^{-2}\) ) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample,

(1).42.2 J

(2). 208.7 J

(3). 104.3 J

(4). 84.5 J

12. The p-V diagram for an ideal gas in a piston cylinder assembly undergoing a thermodynamic process is shown in the figure. The process is

(1).adiabatic

(2). isochoric

(3). isobaric

(4). isothermal

13. Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is

(1).adiabatic

(2). isochoric

(3). isobaric

(4). isothermal

14. In which of the following processes, heat is neither absorbed nor released by a system?

(1).Adiabatic

(2). Isobaric

(3). Isochoric

(4). Isothermal

15. The volume (V) of a monoatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is

(1).1/3

(2). 2/3

(3). 2/5

(4). 2/7

16. Thermodynamic processes are indicated in the following diagram

Match the following:

(1).\(P\rightarrow a\), \(Q\rightarrow c\), \(R\rightarrow d\), \(S\rightarrow b\)

(2). \(P\rightarrow c\), \(Q\rightarrow a\), \(R\rightarrow d\), \(S\rightarrow b\)

(3). \(P\rightarrow c\), \(Q\rightarrow d\), \(R\rightarrow b\), \(S\rightarrow a\)

(4). \(P\rightarrow d\), \(Q\rightarrow b\), \(R\rightarrow a\), \(S\rightarrow c\)

17. A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half.

(1).compressing the gas through adiabatic process will require more work to be done.

(2). compressing the gas isothermally or adiabatically will require the same amount of work.

(3). which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

(4). compressing the gas isothermally will require more work to be done.

18. A Carnot engine having an efficiency of 110 as heat engine, is used as a refrigerator. If the workdone on the systemis 10 J, the amount of energy absorbed from the reservoir at lower temperature is

(1).1 J

(2). 90 J

(3). 99 J

(4). 100 J

19. A refrigerator works between 4°C and 30°C. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant.The power required is (Take, 1 cal =4.2Joules)

(1).23.65 W

(2). 236.5 W

(3). 2365 W

(4). 2.365 W

20. The temperature inside a refrigerator is \(t_2\) °C and the room temperature is \(t_1\) °C. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be

(1).\(\frac{t_1}{t_1-t_2}\)

(2). \(\frac{t_1 + 273}{t_1-t_2}\)

(3). \(\frac{t_2 + 273}{t_1-t_2}\)

(4). \(\frac{t_1 + t_2}{t_1 + 273}\)

21. A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system in the cycle is

(1).p₀V₀

(2). 2p₀V₀

(3). p₀V₀/2

(4). zero

22. A monoatomic gas ata pressure p, having a volume V expands isothermally to a volume 2 V and then adiabatically to a volume 16 V. The final pressure of the gas is (take \(\gamma = \frac{5}{3}\))

(1).64p

(2). 32p

(3). p/64

(4). 16p

23. A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is:

(1).-90 J

(2). -60 J

(3). zero

(4). 30 J

24. A cup of coffee cools from \(90^\circ C\) to \(80^\circ C\) in t minutes, when the room temperature is \(20^\circ C\). The time taken by a similar cup of coffee to cool from \(80^\circ C\) to \(60^\circ C\) at a room temperature same at \(20^\circ C\) is

(1).\(\displaystyle \frac{5}{13}\, t\)

(2). \(\displaystyle \frac{13}{10}\, t\)

(3). \(\displaystyle \frac{13}{5}\, t\)

(4). \(\displaystyle \frac{10}{13}\, t\)

25. The quantities of heat required to raise the temperarture of two solid copper spheres of radii \(r_1\) and \(r_2\) (\(r_1\,=\,1.5\,r_2\)) through 1 K are in the ratio

(1).9/5

(2). 3/2

(3). 5/3

(4). 27/8

26. The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is

(1).12.5%

(2). 6.25%

(3). 20%

(4). 26.80%

27. Figure below shows two paths that may be taken by a gas to go from a state A to a state C.

In process AB, 400 J of heat is added to the system and in process BC, 100 J of heat is added to the system. The heat absorbed by the system in the process AC will be

(1).380 J

(2). 500 J

(3). 460 J

(4). 300 J

28. A carnot engine, having an efficiency of \(\displaystyle \eta\,=\,\frac{1}{10}\) as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservior at lower temperature is

(1).100 J

(2). 99 J

(3). 90 J

(4). 1 J

29. One mole of an ideal diatomic gas undergoes a transition from A to B a transition from A to B along a path AB as shown in the figure,

The change in internal energy of the gas during the transition is:

(1).20kJ

(2). -20kJ

(3). 20J

(4). -12kJ

30. Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius \(\text{r}_\text{A}\) and \(\text{r}_\text{B}\), respectively. On supplyig an equal amount of heat to both the systems reversibly under constant presurre, the pistons of gas A nd B are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ration \(\displaystyle \frac{\text{r}_\text{A}}{\text{r}_\text{B}}\) is equal to

(1).\(\displaystyle \frac{\sqrt{3}}{2}\)

(2). \(\displaystyle \frac{4}{3}\)

(3). \(\displaystyle \frac{3}{4}\)

(4). \(\displaystyle \frac{2}{\sqrt{3}}\)

31. A container has two chambers of volumes \(\text{V}_1\,=\, 2\,\text{litres}\) and \(\text{V}_2\,=\, 3\,\text{litres}\) separated by a partition made of a thermal insulator. The chambers contain n1 = 5 and n2 = 4 moles of ideal gas at pressure p1 = 1 and p2 = 2 atm, respectively. When the partition is removed, the mixture attains equilibrium pressure of

(1).1.8 atm

(2). 1.3 atm

(3). 1.6 atm

(4). 1.4 atm

32. An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressures at temperature \(27^\circ\ \text{C}\). The mass of oxygen withdrawn from the cylinder is nearly equal to:
[Given, \(\text{R}\,=\, \frac{100}{12}\text{J mol}^{-1}\text{K}^{-1}\) and molecular mass of \(\text{O}_2\,=\, 32\), 1 atm pressure \(=\,1.01 \times 10^5 \text{N/m}\)]

(1).0.156 kg

(2). 0.125 kg

(3). 0.144 kg

(4). 0.116 kg