A Carnot engine with efficiency $$50 \%$$ takes heat from a source at $$600 \mathrm{~K}$$. To increase the efficiency to $$70 \%$$, keeping the temperature of the sink same, the new temperature of the source will be

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 $$)$$