The ratio of the specific heats $${{{C_v}} \over {{C_p}}} = {1 \over \gamma }$$ in terms of degrees of freedom (n) is given by

A black body radiates energy at the rate E Wm^$$-$$2 at high temperature TK. When the temperature is reduced to $$\left( {{T \over 4}} \right)$$ K, the new radiant energy is

In an adiabatic process, where pressure is decreased by $${3 \over 4}$$%, if $${{{C_p}} \over {{C_v}}} = {4 \over 3}$$, then the volume increases by

A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is