$A$ sample of $0.1 \, g$ of water at $100^{\circ} C$ and normal pressure $(1.013 \times 10^5 \, N m^{-2})$ requires $54 \, cal$ of heat energy to convert to steam at $100^{\circ} C$. If the volume of the steam produced is $167.1 \, cc$,the change in internal energy of the sample is ....... $J$.

Consider one mole of perfect gas in a cylinder of unit cross-section with a piston attached as shown in the figure. $A$ spring (spring constant $k$) is attached (unstretched length $L$) to the piston and to the bottom of the cylinder. Initially,the spring is unstretched and the gas is in equilibrium. $A$ certain amount of heat $Q$ is supplied to the gas,causing an increase in volume from $V_0$ to $V_1$.
$(a)$ What is the initial pressure of the system?
$(b)$ What is the final pressure of the system?
$(c)$ Using the first law of thermodynamics,write down a relation between $Q, V_0, V_1, P_a$ and $k$.

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas molecules release $20 \ J$ of heat and $10 \ J$ of work is done on the gas. If the initial internal energy of the gas was $40 \ J$,then the final internal energy will be ........ $J$.

The first law of thermodynamics is concerned with the conservation of

$A$ resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. $A$ current $i$ flows through the coil which has a resistance $R$. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.