In a cyclic process,the work done by the system is

If $150 \ J$ of heat is added to a system and the work done by the system is $110 \ J$,then the change in internal energy will be .......... $J$.

The $p-V$ diagram of a system undergoing thermodynamic changes is as shown in the figure. The work done by the system in going from $A \rightarrow B \rightarrow C$ is $30 \,J$. If $68 \,J$ of heat is given to the system,then the change in the internal energy of the system between $A$ and $C$ is (in $\,J$)

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 $k$.

When a system is taken from thermodynamic state $i$ to $f$ along the path $iaf$ (see figure),it is found that the heat $Q$ absorbed by the system is $50 \ cal$ and the work $W$ done by the system is $20 \ cal$. Along the path $ibf$,$Q = 36 \ cal$. What is the work $W$ done along the path $ibf$ (in $cal$)?

Write and explain the first law of thermodynamics.