The r.m.s. speed of hydrogen at S.T.P. is '$u$' $\text{m/s}$. If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively

An ideal gas is heated from $27^\circ\text{C}$ to $627^\circ\text{C}$ at constant pressure. If initial volume of gas is $4\ \text{m}^3$, then the new volume of the gas will be

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