A cylindrical rod has temperatures '$$T_1$$' and '$$T_2$$' at its ends. The rate of flow of heat is '$$Q_1$$' cal $$\mathrm{s}^{-1}$$. If length and radius of the rod are doubled keeping temperature constant, then the rate of flow of heat '$$\mathrm{Q}_2$$' will be

The initial pressure and volume of a gas is '$$\mathrm{P}$$' and '$$\mathrm{V}$$' respectively. First by isothermal process gas is expanded to volume '$$9 \mathrm{~V}$$' and then by adiabatic process its volume is compressed to '$$\mathrm{V}$$' then its final pressure is (Ratio of specific heat at constant pressure to constant volume $$=\frac{3}{2}$$)

If $$\mathrm{m}$$' represents the mass of each molecules of a gas and $$\mathrm{T}$$' its absolute temperature then the root mean square speed of the gas molecule is proportional to

An ideal gas at pressure '$$p$$' is adiabatically compressed so that its density becomes twice that of the initial. If $$\gamma=\frac{c_p}{c_v}=\frac{7}{5}$$, then final pressure of the gas is