When $2 \ kg$ of water is boiled at atmospheric pressure,it converts into steam. The volume increases from $2 \times 10^{-3} \ m^3$ to $3.34 \ m^3$. The work done by the system is ....... $kJ$.

$A$ 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 $\,J$)

$Assertion:$ The heat supplied to a system is always equal to the increase in its internal energy.
$Reason:$ When a system changes from one thermal equilibrium to another,some heat is absorbed by it.

$1 \, kg$ of a gas does $20 \, kJ$ of work and receives $16 \, kJ$ of heat when it is expanded between two states. $A$ second kind of expansion can be found between the initial and final states which requires a heat input of $9 \, kJ$. The work done by the gas in the second expansion is ....... $kJ$.

The change in the internal energy of a mass of gas,when the volume changes from $V$ to $2V$ at constant pressure $P$,is (where $\gamma$ is the ratio of specific heat of gas at constant pressure to specific heat at constant volume):

$A$ gas is taken from state $A$ to state $B$ along two different paths $1$ and $2$. The heat absorbed and work done by the system along these two paths are $Q_1, Q_2$ and $W_1, W_2$ respectively. Then: