In an external environment of temperature ($T$) kelvin, a sphere at temperature ($3T$) kelvin has cooling rate $R_1$. When the temperature of that sphere falls to ($2T$) kelvin, the cooling rate $R_2$ of the sphere will become

'$x$' joule of heat is incident on a body. Out of it, the total heat reflected and transmitted by it is '$y$' joule. The absorption coefficient of the body is

Consider two rods 1 and 2 of same length. They have different specific heats $(C_1, C_2)$, thermal conductivities $(K_1, K_2)$ and area of cross-section $(A_1, A_2)$ respectively. Both the rods have temperatures $(T_1, T_2)$ at their ends. If their rate of loss of heat due to conduction is equal, then

A Carnot engine, whose efficiency is 40% takes heat from a source maintained at temperature 600K. To have an efficiency 60%, the intake temperature for the same exhaust temperature should be