Two moles of helium are mixed with n moles of hydrogen. If $${{Cp} \over {Cv}} = {3 \over 2}$$ for the mixture, then the value of n is :

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.

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 ]

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 $${{{\eta _B}} \over {{\eta _A}}}$$ ?