Thermodynamics

Three copper blocks of masses M₁, M₂ and M₃ kg respectively are brought into thermal contact till they reach equilibrium. Before contact, they were at T₁, T₂, T₃ (T₁ > T₂ > T₃ ). Assuming there is no heat loss to the surroundings, the equilibrium temperature T is (s is specific heat of copper)

(a) T= $\frac{{\mathit{T}}_1+{\mathit{T}}_2+{\mathit{T}}_3}{3}$

(b) T= $\frac{{\mathit{M}}_1{\mathit{T}}_1+{\mathit{M}}_2{\mathit{T}}_2+{\mathit{M}}_3{\mathit{T}}_3}{{\mathit{M}}_1+{\mathit{M}}_2+{\mathit{M}}_3}$  

(c)  T= $\frac{{\mathit{M}}_1{\mathit{T}}_1+{\mathit{M}}_2{\mathit{T}}_2+{\mathit{M}}_3{\mathit{T}}_3}{3({\mathit{M}}_1+{\mathit{M}}_2+{\mathit{M}}_3)}$

(d) T= $\frac{{\mathit{M}}_1{\mathit{T}}_1\mathit{s}+{\mathit{M}}_2{\mathit{T}}_2\mathit{s}+{\mathit{M}}_3{\mathit{T}}_3\mathit{s}}{{\mathit{M}}_1+{\mathit{M}}_2+{\mathit{M}}_3}$   

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

(a) $2^{\mathit{\gamma }-1}$  

(b) ${\left(\frac{1}{2}\right)}^{\mathit{\gamma }-1}$   

(c) $({\frac{1}{1-\mathit{\gamma }})\mathit{}\mathit{}}^2$  

(d) ${\left(\frac{1}{\mathit{\gamma }-1}\right)}^2$  

An ideal gas undergoes cyclic process ABCDA as shown in given P-V diagram (Fig. 12.4). The amount of work done by the gas is

(a) 6 P_oV_o

(b) –2 P_oV_o

(c) + 2 P_oV_o

(d) + 4 P_oV_o

Consider P-V diagram for an ideal gas shown in Out of the following diagrams , which represents the T-P diagram?

If an average person jogs, he produces 14.5 × 10³ cal/min. This is removed by the evaporation of sweat. The amount of sweat evaporated per minute (assuming 1 kg requires 580 × 10³ cal for evaporation) is

(a) 0.25 kg

(b) 2.25 kg

(c) 0.05 kg

(d) 0.20 kg

An ideal gas undergoes four different processes from the same initial state (Fig. 12.1). Four processes are adiabatic, isothermal, isobaric and isochoric. Out of 1, 2, 3 and 4 which one is adiabatic.

(a) 4

(b) 3

(c) 2

(d) 1

The initial state of a certain gas is (Pi , Vi , Ti ). It undergoes expansion till its volume becomes V_f . Consider the following two cases:

(a) The expansion takes place at constant temperature.

(b) The expansion takes place at constant pressure. Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas more?

If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature (27 °C), find the temperature inside the refrigerator.

In a refrigerator one removes heat from a lower temperature and deposits to the surroundings at a higher temperature. In this process, mechanical work has to be done, which is provided by an electric motor. If the motor is of 1kW power, and heat is transferred from –3°C to 27°C, find the heat taken out of the refrigerator per second assuming its efficiency is 50% of a perfect engine.

Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump ?V V ( ) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P₁ to P₂?