The ratio of vapour densities of two gases at the same temperature is $ \frac{4}{25} $, then the ratio of r.m.s. velocities will be :

The kinetic energy of translation of the molecules in 50 g of $ \text{CO}_2 $ gas at 17°C is :

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

A Carnot engine $(\mathrm{E})$ is working between two temperatures 473 K and 273 K . In a new system two engines - engine $E_1$ works between 473 K to 373 K and engine $E_2$ works between 373 K to 273 K . If $\eta_{12}, \eta_1$ and $\eta_2$ are the efficiencies of the engines $E, E_1$ and $E_2$, respectively, then