A piece of metal at $$850 \mathrm{~K}$$ is dropped in to $$1 \mathrm{~kg}$$ water at $$300 \mathrm{~K}$$. If the equilibrium temperature of water is $$350 \mathrm{~K}$$ then the heat capacity of the metal, expressed in $$\mathrm{JK}^{-1}$$ is $$(1 \mathrm{~cal}=4.2 \mathrm{~J})$$

Heat energy is incident on the surface at the rate of X J/min . If '$$a$$' and '$$r$$' represent coefficient of absorption and reflection respectively then the heat energy transmitted by the surface in '$$t$$' minutes is

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is $$\left(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\gamma=\frac{3}{2}\right) \quad(\mathrm{R}=$$ gas constant $$)$$

An ideal gas in a container of volume 500 c.c. is at a pressure of $$2 \times 10^{+5} \mathrm{~N} / \mathrm{m}^2$$. The average kinetic energy of each molecule is $$6 \times 10^{-21} \mathrm{~J}$$. The number of gas molecules in the container is