One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

Two moles of an ideal monatomic gas occupies a volume V at 27^oC. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two energies A and B are represented by $${\eta _A}$$ and $${\eta _B},$$ respectively, then what is the value of $${{{\eta _B}} \over {{\eta _A}}}$$ ?

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms^-1 is :
[k_B =1.4 $$ \times $$ 10^-23 J/K; m_He = 7 $$ \times $$ 10 ^-27 kg ]