$A$ gas is allowed to expand in an insulated container against a constant external pressure of $2.5 \ bar$ from $4.5 \ dm^3$ to $7 \times 10^{-3} \ m^3$. What is the change in internal energy of the gas (in $J$)?

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:

Derive the relationship between $\Delta H$ and $\Delta U$ for an ideal gas. Explain each term involved in the equation.

$A$ gas performs $0.320 \ kJ$ work on the surrounding and absorbs $120 \ J$ of heat from the surrounding. Hence,the change in internal energy is: (in $J$)

For the reaction,$C_3H_{8(g)} + 5O_{2(g)} \to 3CO_{2(g)} + 4H_2O_{(l)}$ at constant temperature,$\Delta H - \Delta E$ is

The work done to contract a gas in a cylinder is $462 \, J$. $128 \, J$ of energy is evolved in the process. What will be the internal energy change in the process? (in $J$)