$A$ system receives $100 \ cal$ of heat,and at the same time,$50 \ cal$ of work is done by the system. Calculate the change in internal energy. (in $cal$)

$A$ gas absorbs $200 \ J$ of heat and expands by $500 \ cm^3$ against a constant external pressure of $2 \times 10^5 \ N \ m^{-2}$. What is the change in internal energy (in $J$)?

Three moles of an ideal gas are compressed isothermally from $60 \ L$ to $20 \ L$ using a constant external pressure of $5 \ atm$. The heat exchange $Q$ for the compression is $....... \ L \cdot atm$.

For which of the following reactions is $\Delta H \neq \Delta U$?

Explain the relationship between the change in heat at constant pressure and constant volume.

What is the amount of work done when $0.5 \ mol$ of methane,$CH_{4(g)}$,is subjected to combustion at $300 \ K$? (Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)