$A$ source supplies heat to a system at the rate of $1000 \, W$. If the system performs work at a rate of $200 \, W$,the rate at which the internal energy of the system increases is $....... \, W$.

The internal energy change in a system that has absorbed $2 \; kcal$ of heat and done $500 \; J$ of work is ...... $J$.

$1\;g$ of water,of volume $1\;cm^{3}$ at $100^{\circ}C$,is converted into steam at the same temperature under normal atmospheric pressure $(=1 \times 10^{5}\;Pa)$. The volume of steam formed equals $1671\;cm^{3}$. If the specific latent heat of vaporisation of water is $2256\;J/g$,the change in internal energy is.....$J$.

$A$ cylinder with a piston of unit cross-sectional area contains one mole of an ideal gas as shown in the figure. $A$ spring of unstretched length $L$ and spring constant $K$ is connected between the piston and the bottom of the cylinder. Initially, the spring is unstretched and the gas is in equilibrium. When an amount of heat $Q$ is supplied to the gas, its volume changes from $V_0$ to $V_1$. Find:
$(a)$ The initial pressure of the system.
$(b)$ The final pressure of the system.
$(c)$ Using the first law of thermodynamics, find the relation between $Q, V_0, V_1, P_a$ and $K$.

The latent heat of vaporisation of water is $2240 \, J/g$. If the work done in the process of expansion of $1 \, g$ of water is $168 \, J$,then the increase in internal energy is ....... $J$.

$A$ gas is expanded from an initial state to a final state along a path that consists of $(a)$ an isothermal expansion doing $40 \,J$ work,$(b)$ an adiabatic expansion doing $W$ work,$(c)$ an isothermal expansion doing $30 \,J$ work. If the total change in the internal energy of the gas is $-20 \,J$,the work done by the gas during the adiabatic expansion $W=$ (in $\,J$)