When a system is taken from state $i$ to a state $f$ along path $iaf$,$Q = 50 \, J$ and $W = 20 \, J$. Along path $ibf$,$Q = 35 \, J$. If $W = -13 \, J$ for the curved return path $fi$,$Q$ for this path is ...... $J$.

During the melting of a slab of ice at $273 \ K$ at atmospheric pressure,

$200\,g$ of water is heated from $40\,^{\circ}C$ to $60\,^{\circ}C$. Ignoring the slight expansion of water,the change in its internal energy is close to ...... $kJ$ (Given specific heat of water $= 4184\,J/kg\cdot K$)

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

$1 \, kg$ 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 heat supplied to a gas at a constant pressure of $5 \times 10^5 \ Pa$ is $1000 \ kJ$. If the volume of gas changes from $1 \ m^3$ to $2.5 \ m^3$,then the change in internal energy of the gas is (in $kJ$)