The rate of flow of heat through a metal rod with temperature difference $$40^{\circ} \mathrm{C}$$ is $$1600 \mathrm{~cal} / \mathrm{s}$$. The thermal resistance of metal rod in $${ }^{\circ} \mathrm{C} \mathrm{s} / \mathrm{cal}$$ is

If the temperature of a hot body is increased by $$50 \%$$, then the increase in the quantity of emitted heat radiation will be approximately

A monoatomic gas at pressure '$$\mathrm{P}$$', having volume '$$\mathrm{V}$$' expands isothermally to a volume '$$2 \mathrm{~V}$$' and then adiabatically to a volume '$$16 \mathrm{~V}$$'. The final pressure of the gas is (Take $$\gamma=5 / 3$$ )

A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$$ is its initial volume. The initial temperature of the gas is $$T_i$$ in Kelvin and the final temperature is '$$x T_i$$'. The value of '$$x$$' is