The energy spectrum of a black body exhibits a maximum around a wavelength '$\lambda$'. The temperature of the black body is now changed such that the energy is maximum around a wavelength $2\lambda/3$. The power radiated by the black body will now increase by a factor

A black rectangular surface of area 'A' emits energy 'E' per second at $27^\circ$C. If length and breadth is reduced to half of its initial value and temperature is raised to $327^\circ$C then energy emitted per second becomes

A monoatomic gas at pressure P having volume V expands isothermally to a volume 3V and then adiabatically to a volume 81 V. The final pressure of the gas is ($\gamma = 5/3$).

An ideal gas at $27^\circ$C is compressed adiabatically to $\left(\dfrac{8}{27}\right)$ of its original volume. If $\gamma = 5/3$, then the rise in temperature of a gas is