The average force applied on the walls of a closed container depends on $$T^x$$ where $$T$$ is the temperature of an ideal gas. The value of '$$x$$' is

A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is $$\mathrm{E}$$. Now due to change in temperature of that body, it radiates maximum energy at wavelength $$\frac{2 \lambda}{3}$$. At that temperature emissive power is

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

The amplitude of a particle executing S.H.M. is $$3 \mathrm{~cm}$$. The displacement at which its kinetic energy will be $$25 \%$$ more than the potential energy is