$A$ gas is supplied with $1500 \; J$ of heat energy at constant pressure. If the constant pressure of the gas is $2.1 \times 10^{5} \; N/m^{2}$ and the increase in volume is $2.5 \times 10^{-3} \; m^{3}$,then the increase in the internal energy of the gas is ...... $J$.

The first law of thermodynamics is a special case of which law?

If $Q$,$E$,and $W$ denote respectively the heat added,change in internal energy,and the work done by a closed cycle process,then

$A$ cylinder with a piston of unit cross-sectional area contains one mole of an ideal gas as shown in the figure. $A$ spring of unstretched length $L$ and spring constant $K$ is connected between the piston and the bottom of the cylinder. Initially, the spring is unstretched and the gas is in equilibrium. When an amount of heat $Q$ is supplied to the gas, its volume changes from $V_0$ to $V_1$. Find:
$(a)$ The initial pressure of the system.
$(b)$ The final pressure of the system.
$(c)$ Using the first law of thermodynamics, find the relation between $Q, V_0, V_1, P_a$ and $K$.

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 ...... $J$.

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$ : If $dQ$ and $dW$ represent the heat supplied to the system and the work done on the system respectively,then according to the first law of thermodynamics $dQ = dU - dW$.
Reason $R$ : The first law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements,choose the correct answer from the options given below: