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

The heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by $48\ ^\circ\text{C}$ at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(\text{N}_2)$ = 28)

The speeds of the seven molecules are 1, 3, 5, 7, 2, 4 and 6 km/s respectively. The ratio of their r.m.s. velocity and average velocity will be