When $x \ kJ$ heat is provided to a system,work equivalent to $y \ J$ is done on it. What is the internal energy change during this operation?

$A$ gas is allowed to expand in an insulated container against a constant external pressure of $10 \ atm$ from an initial volume $4.2 \ L$ to $5.2 \ L$. The change in internal energy $\Delta E$ of the gas will be $:-$

During the free expansion of an ideal gas in an isolated chamber,

Calculate the internal energy change of one mole of an ideal gas during an adiabatic free expansion process from a volume of $2 \ L$ to $5 \ L$.

An engine absorbs heat $Q_1$ at temperature $T_1$ and heat $Q_2$ at temperature $T_2$. The work done by the engine is given as $W = Q_1 + Q_2$. Which of the following statements is correct?

What is the final temperature of $0.10 \ mol$ monoatomic ideal gas that performs $75 \ cal$ of work adiabatically if the initial temperature is $227 \ ^\circ C$? (Use $R = 2 \ cal \cdot K^{-1} \cdot mol^{-1}$)