The internal energy change in a system that has absorbed $2 \, kcal$ of heat and done $500 \, J$ of work 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 $k$.

When unit mass of water boils to become steam at $100\,^{\circ}C$,it absorbs $Q$ amount of heat. The densities of water and steam at $100\,^{\circ}C$ are $\rho_1$ and $\rho_2$ respectively and the atmospheric pressure is $p_0$. The increase in internal energy of the water is:

The first law of thermodynamics can be written as $\Delta U = \Delta Q + \Delta W$ for an ideal gas. Which of the following statements is correct?

$A$ perfect gas goes from state $A$ to another state $B$ by absorbing $8 \times 10^5 \ J$ of heat and doing $6.5 \times 10^5 \ J$ of external work. It is now transferred between the same two states in another process in which it absorbs $10^5 \ J$ of heat. Then in the second process:

If the heat given to a system is $35 \ J$ and the work done on the system is $15 \ J$,then the change in the internal energy of the system is ... $J$?