$A$ 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 $cal$)

$2 \ mol$ of an ideal gas are expanded isothermally and reversibly from $20 \ L$ to $40 \ L$ at $300 \ K$. Calculate work done. $(R=8.314 \ J \ K^{-1} \ mol^{-1})$ (in $J$)

For the reaction $CH_3COOH_{(l)} + 2O_{2(g)} \rightleftharpoons 2CO_{2(g)} + 2H_2O_{(l)}$ at $25\,^{\circ}C$ and $1\,atm$ pressure,$\Delta H = -874\,kJ.$ Then the change in internal energy $(\Delta E)$ is $...\,kJ$

For an isochoric process,the first law of thermodynamics can be expressed as:

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?

When a gas undergoes adiabatic expansion,it cools down because: