A black body radiates maximum energy at wavelength '$\lambda$' at temperature $T_1$ and its emissive power is E. When the temperature of the body is changed to $T_2$, it radiates maximum energy at wavelength $\dfrac{2\lambda}{3}$, then the emissive power will become

A body cools from a temperature $3\theta$ to $2\theta$ in 10 minute. The room temperature is $\theta$. The temperature of the body at the end of the next 10 minute is '$x$'. Assuming that Newton's law of cooling is applicable, the value of '$x$' will be

An ideal monoatomic gas is taken around the cycle ABCDA as shown in the P.V diagram. The work done during the cycle is

An ideal gas with pressure P, volume V and temperature T is expanded isothermally to volume 2V and a final pressure $P_i$. The same gas is expanded adiabatically to a volume 2V then the final pressure is $P_a$. In terms of $\gamma$, the ratio of the two specific heats for the gas, the ratio $P_i / P_a$ is