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

A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $$\gamma=1.5$$, then the final pressure is