The efficiency of Carnot engine which operates between the two temperatures $T_1 = 500$ K and $T_2 = 300$ K is

An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally, to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $\dfrac{P_A}{P_I}$ is $\left(\dfrac{C_P}{C_V} = \gamma\right)$

A sphere is at temperature $600$ K. In an external environment of $200$ K, its cooling rate is R. When the temperature of the sphere falls to $400$ K then cooling rate R' will become

Two rods of same length, radius and material transfer a given amount of heat in 't' second when they are joined as shown in fig (1). But when they are joined as shown in fig (2) then they will transfer same heat in same condition in time