An ideal gas at $27^\circ$C is compressed adiabatically to $\left(\dfrac{8}{27}\right)$ of its original volume. If $\gamma = 5/3$, then the rise in temperature of a gas is

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled by

The ratio of the thermal conductivity of two rods of different materials is 6:5. The two rods of same area of cross section and same thermal resistance will have the length in the ratio

A black rectangular surface of area A emits energy E per second at $127^\circ$C. If length and breadth is reduced to half of initial value and temperature is raised to $527^\circ$C then energy emitted becomes