Which of the following relations is correct for the internal energy change $(\Delta U)$ in a process occurring at constant volume?

$A$ gas occupies $2 \ L$ at $S.T.P.$ It is supplied with $300 \ J$ of heat,causing its volume to expand to $2.5 \ L$ against an external pressure of $1 \ atm$. What is the change in internal energy in $J$?

Assuming all reactions occur in an open vessel,for which reaction will $\Delta H = \Delta U$?

In ...... process,work is done at the expense of internal energy.

$1 \, \text{mole}$ of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ}C$. The work done is $3 \, \text{kJ} \, \text{mol}^{-1}$. The final temperature of the gas is $...... \text{K}$ (Nearest integer). Given $C_{V} = 20 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1}$.

The conservation of mass and energy is demonstrated by: