Three identical heat conducting rods are connected in series as shown in the figure. The rods on the side have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state, temperature at the left junction is $T_1$ and that at the right junctions is $T_2$. The ratio $T_1/T_2$ is

A wire of length $L$ and diameter $d$ is used in a bulb. The temperature of wire is $T$ and power radiated by the wire is $P$. Its emissivity is ($\sigma$ = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)

The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\dfrac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be

An ideal gas undergoes cyclic process ABCDA as shown in given p-V diagram. What is the magnitude of amount of work done by the gas?