Two moles of an ideal monoatomic gas are allowed to expand adiabatically and reversibly from $300 \ K$ to $200 \ K$. The work done in the system is $... \ kJ$ $(C_V = 12.5 \ J/K/mol)$.

An ideal gas expands against a constant external pressure of $2 \ bar$ from $5 \ L$ to $8 \ L$ and absorbs $10 \ kJ$ of heat. What is $\Delta U$ of the system (in $J$)?

Based on the first law of thermodynamics,which of the following is correct?

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these processes are:
$Q_1 = 6000 \, J, Q_2 = -5500 \, J, Q_3 = -3000 \, J, Q_4 = 3500 \, J$
$W_1 = 2500 \, J, W_2 = -1000 \, J, W_3 = -1200 \, J, W_4 = x \, J$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $|x|$ and $\eta$ respectively are:

Which of the following is the correct mathematical expression for the first law of thermodynamics?

$q$ and $w$ are both ....... functions and $q + w$ is a ....... function.