When a system is taken from state $i$ to state $f$ along the path $iaf$,it is found that $Q = 50 \ cal$ and $W = 20 \ cal$. Along the path $ibf$,$Q = 36 \ cal$. The work done $W$ along the path $ibf$ is ....... $cal$.

The change in internal energy when $20 \,g$ of a gas is heated from $25^{\circ} C$ to $35^{\circ} C$ at constant volume is (Specific heat capacity of the gas at constant volume $C_{v} = 0.2 \,cal \,g^{-1} {}^{\circ} C^{-1}$): (in $\,J$)

$A$ given quantity of gas is taken from $A$ to $C$ in two ways: $a$) directly from $A \rightarrow C$ along a straight line, and $b$) in two steps, from $A \rightarrow B$ and then from $B \rightarrow C$. The work done and heat absorbed along the direct path $A \rightarrow C$ are $200 \ J$ and $280 \ J$ respectively. If the work done along the path $A \rightarrow B \rightarrow C$ is $80 \ J$, find the heat absorbed along this path.

An ideal gas is contained in a thermally insulated rigid container. It is heated by a filament of $100 \, \Omega$ resistance by passing a current of $1 \, A$ for $5 \, \text{min}$. The change in internal energy 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 $kJ$)

An electric heater supplies heat to a system at a rate of $100 \text{ W}$. If the system performs work at a rate of $75 \text{ J/s}$, then the rate at which internal energy increases will be: (in $\text{ W}$)