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

$1 \,g$ of water at $100^{\circ} C$ is completely converted into steam at $100^{\circ} C$. $1 \,g$ of steam occupies a volume of $1650 \,cc$. (Neglect the volume of $1 \,g$ of water at $100^{\circ} C$). At the pressure of $10^5 \,N/m^2$, the latent heat of steam is $540 \,cal/g$ $(1 \,calorie = 4.2 \,joule)$. The increase in the internal energy (in joule) is:

$1 \, kg$ of a gas does $20 \, kJ$ of work and receives $16 \, kJ$ of heat when it is expanded between two states. $A$ second kind of expansion can be found between the initial and final states which requires a heat input of $9 \, kJ$. The work done by the gas in the second expansion is ....... $kJ$.

$A$ system is taken from state $A$ to state $B$ along two different paths. The heat absorbed and work done by the system along these two paths are $Q_1, Q_2$ and $W_1, W_2$ respectively,then

Write the sign convention for internal energy in thermodynamics.

$A$ container contains $1 \text{ mole}$ of a gas with molar mass $M$ and adiabatic index $\gamma = C_P/C_V$. The container is moving with a velocity $v$. When it suddenly stops,the kinetic energy of the container is converted into the internal energy of the gas. The rise in the temperature of the gas is: