When heat energy of $1500 \; J$ is supplied to a gas at a constant pressure of $2.1 \times 10^5 \; N/m^2$,its volume increases by $2.5 \times 10^{-3} \; m^3$. The increase in the internal energy of the gas in Joules is ...... $J$.

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 $k$.

$A$ 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 $....... \, W$.

Which of the following laws of thermodynamics defines the term internal energy?

First law of thermodynamics is represented by

$A$ system is given $300$ calories of heat and it does $600$ joules of work. How much does the internal energy of the system change in this process? $(J = 4.18 \text{ Joules/cal})$ (in joule)