For a thermodynamic process $\delta Q = -50 \text{ calorie}$ and $W = -20 \text{ calorie}$. If the initial internal energy is $-30 \text{ calorie}$,then the final internal energy will be ....... $\text{calorie}$.

$A$ 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 $K$.

The $P-V$ diagram of a system undergoing a thermodynamic transformation is shown in the figure. The work done by the system in going from $A \to B \to C$ is $30 \ J$ and $40 \ J$ of heat is given to the system. The change in internal energy between $A$ and $C$ is ....... $J$.

When $150 \ J$ of heat is supplied to a system,the work done by the system is $110 \ J$. The change in the internal energy of the system is ....... $J$.

$200\,g$ 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 first law of thermodynamics states that: