Hydrogen gas is undergoing a process given by $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is

$Q$ amount of heat is given to $0.5 \text{ mole}$ of an ideal mono-atomic gas by a process $TV^n = \text{constant}$. The following graph shows the variation of temperature with $Q$. Find the value of $n$.

$P_i, V_i$ and $P_f, V_f$ are initial and final pressures and volumes of a gas in a thermodynamic process respectively. If $PV^n = \text{constant}$, then the amount of work done is

An ideal gas is subjected to a thermodynamic process $PV^{2.5} = 0.40$,where $P$ is in $Pa$ and $V$ is in $m^3$. What is the slope of the $P-V$ curve with volume plotted against the $x-$axis at $V = 1 \, m^3$?

$A$ gas is found to obey the law $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$,its final temperature becomes

During an experiment, an ideal gas obeys an additional equation of state $P^2V = \text{constant}$. The initial temperature and volume of the gas are $T$ and $V$ respectively. When it expands to volume $2V$, its temperature will be: