Two soap bubbles, A and B, have radii in the ratio $3 : 2$. The excess pressure inside the bubble A to that of B is in the ratio

A black body emits radiation of maximum intensity of wavelength '$\lambda$' at temperature 'T' K. Its corresponding wavelength at temperature $(2.5T)$ K will be

In a composite slab there are two materials having coefficients of thermal conductivity K and 2K, thickness x and 4x repectively. The temperature of the two outer surfaces of a composite slab are $T_2$ and $T_1$ $(T_2 > T_1)$. $T_2$ is on side K and $T_1$ is on side 2K. The rate of heat transfer through the slab in a steady state is $\left[\dfrac{A(T_2 - T_1)K}{x}\right] \cdot f$, where f is equal to

A carnot engine having efficiency $\dfrac{1}{6}$, operates between the source temperature $T_H$ and the sink temperature $T_C$. Its efficiency increases to $\dfrac{1}{3}$, when $T_C$ is decreased by 64 K. The temperatures $T_H$ and $T_C$ are repectively