An ideal gas undergoes a process in which its pressure P and volume V are related by $PV^n = constant$, where n is a constant. If the gas expands adiabatically ($n = \gamma$, where $\gamma = C_P/C_V$), which of the following statements is TRUE regarding the work done by the gas?

10 g each of ${\rm{C}}{{\rm{H}}_4}\,\,{\rm{and}}\,\,{{\rm{O}}_2}$ are kept in cylinders of same volume under same temperatures, give the pressure ratio of two gases

A sample of gas at 35\,^\circ C and 1 atmospheric pressure occupies a volume of $3.75\,\,{\rm{litre}}$. At what temperature should the gas be kept, if it is required to reduce the volume to $3.0$ litre at the same pressure?

A closed vessel contains equal number of nitrogen and oxygen molecules at a pressure of $P$ mm. If nitrogen is removed from the system, then the pressure will be:

$5\,{\rm{g}}$ each of the following gases at 87\,^\circ C and $750\,{\rm{mm}}$ pressure are taken. Which of them will have the least volume?

At what temperature will the volume of a gas at 0\,^\circ C double itself, pressure remaining constant?

An ideal gas expands according to $PV =$ constant. On expansion, the temperature of gas:

If volume of a given mass of gas at constant $T$, becomes three times, the pressure will be:

The equation of state corresponding to 8g of ${{\rm{O}}_2}$ is

A mixture of 2 moles of He and 1 mole of $N_2$ is contained in a 10 L vessel at 27°C. What is the partial pressure of nitrogen?

Two identical flasks contain different gases at the same temperature and pressure. Flask A contains $CO_2$ and Flask B contains $H_2$. Which of the following statements is true regarding the average speed of the gas molecules?