The first law of thermodynamics states that:

$A$ given quantity of gas is taken from $A$ to $C$ in two ways: $a$) directly from $A \rightarrow C$ along a straight line, and $b$) in two steps, from $A \rightarrow B$ and then from $B \rightarrow C$. The work done and heat absorbed along the direct path $A \rightarrow C$ are $200 \ J$ and $280 \ J$ respectively. If the work done along the path $A \rightarrow B \rightarrow C$ is $80 \ J$, find the heat absorbed along this path.

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 ... $J$?

$A$ resistance coil connected to an external battery is placed inside an adiabatic cylinder fitted with a frictionless piston and containing an ideal gas. $A$ current $i$ flows through the coil which has a resistance $R$. At what speed must the piston move upward in order that the temperature of the gas remains unchanged? Neglect atmospheric pressure.

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 ....... $\text{calorie}$.

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: