Two identical samples of a gas are allowed to expand $(i)$ isothermally and $(ii)$ adiabatically. The work done is:

The change in internal energy of a given mass of a gas,when its volume changes from $V$ to $3V$ at constant pressure $P$,is (where $\gamma$ is the ratio of the specific heat capacities of the gas).

Check whether the following statements are true or false:
$1.$ The change in internal energy $\Delta U = 0$ in a cyclic process.
$2.$ In an adiabatic process,temperature remains constant.
$3.$ The internal energy of a system during an isothermal process decreases.

$A$ cyclic process for $1 \, \text{mole}$ of an ideal gas is shown in the $V-T$ diagram. Find the work done in processes $AB$, $BC$, and $CA$ respectively.

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to $4$ times its initial volume $(V_0)$, then isobarically compressed to its original volume. Finally, the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

An engineer claims to have made an engine delivering $10 \ kW$ of power with a fuel consumption of $1 \ g/s$. The calorific value of the fuel is $2 \ kcal/g$. Is the claim of the engineer valid?