Steam at $100^{\circ} \mathrm{C}$ is added to 150 g water to increase its temperature from $20^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The total mass of the water at $40^{\circ} \mathrm{C}$ is (specific heat capacity of water $=1 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat of steam $\left.=540 \mathrm{cal} \mathrm{g}^{-1}\right)$

A blacksmith fixes circular iron frame on the wooden wheel of a bullock cart. The diameter of wooden wheel and circular iron frame are 5.012 m and 5 m respectively at $27^{\circ} \mathrm{C}$. The temperature (in ${ }^{\circ} \mathrm{C}$ ) to which iron ring must be heated so as to fit the wooden wheel is

(Coefficient of linear expansion of iron $\left.=1.2 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)$

Two moles of triatomic gas $\left(\gamma=\frac{4}{3}\right)$ at temperature $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume becomes 8 times its initial volume. Later the temperature of the gas is doubled in an isochoric process. The total work done in the two processes is

(Where, R is universal gas constant)

If the temperature of a gas is increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, then the percentage increase in the rms speed of the gas molecules is