An object cools from $100^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 10 min , when the surrounding temperature is $10^{\circ} \mathrm{C}$. Then the time taken by the object to cool from $70^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$ is (take, $\ln 2=0.7, \ln 3=11, \ln 6=18$ )

1.00 kg of liquid water at $100^{\circ} \mathrm{C}$ undergoes a phase change into steam at $100^{\circ} \mathrm{C}$ at 1.0 atm (take it to be $1.00 \times 10^5 \mathrm{~Pa}$ ). The initial volume of the liquid water was $1.00 \times 10^{-3} \mathrm{~m}^3$ which is changed to $2.001 \mathrm{~m}^3$ of steam. Find the change in the internal energy of the system.

(Use heat of vaporisation $\simeq 2000 \mathrm{~kJ} / \mathrm{kg}$ )

A monoatomic gas does 100 J of work, when it is expanded isobarically. How much of heat is given to the gas in the process?

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \mathrm{~m} / \mathrm{s}$, then the rms speed of helium molecule at the same temperature is