A Carnot cycle is performed by 1 mole of air (r = 1.4) initially at 327^o C. Each stage represents a compression or expansion in the ratio 1:6 (a) Calculate the lowest temperature
(b) Calculate network done during each side
(c) Calculate efficiency of the engine
Take R = 8.31 J/ mol^-K

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system in thermally insulated. The stopcock is suddenly opened. Answer the following
(a) What is the change in internal energy of the gas?
(b) What is the change in temperature of the gas?
(c) Do the intermediate states of the system (before settling to the final equilibrium state) lie on its p - V - T surface?

The efficiency of a Carnot engine is 1/2. If the sink temperature is reduced by 100^o C, then engine efficiency becomes 2/3. Find
(i) sink temperature
(ii) source temperature
(iii) Explain, why a Carnot engine cannot have 100% efficiency?

State Carnot theorem. The motor in a refrigerator has power output 250 watt. The freezing compartment is at 270 K and outside air at 300 K. Assuming ideal efficiency, what is the amount of heat that can be extracted from the freezing compartment in 10 minutes? What is the shortest time in which 10 kg of water at 273 K can be converted into ice? J = 4.2 x 10³ J kcal^-1.

When a system is taken from state i to state f along the path iaf, it is found that the heat Q absorbed by the system is 50 cal. and work done W by the system is equal to 20 cal. along the path ibf; Q = 36 cal

(i) What is W along the path ibf?
(ii) If W = -13 cal. for the curved return path fi what is Q for this path?
(iii) Take U, = 10 cal, what is U_f?
(iv) If U_b = 22 cal. what are Q for the processes bf and ib?