Which of the following graphs correctly represents the variation of $\beta = - (dV/dP)/V$ with $P$ for an ideal gas at constant temperature?

The equation of state for $5 \, g$ of oxygen at a pressure $P$ and temperature $T$,when occupying a volume $V$,will be (where $R$ is the gas constant).

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston of cross-section $8.0 \times 10^{-3} \, m^2$. Initially,the gas is at $300 \, K$ and occupies a volume of $2.4 \times 10^{-3} \, m^3$,and the spring is in its relaxed state as shown in the figure. The gas is heated by a small heater until the piston moves out slowly by $0.1 \, m$. The force constant of the spring is $8000 \, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless,and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible.) (in $, K$)

$A$ graph between volume $V$ and absolute temperature $T$ is obtained when a given mass of a gas is heated. During the heating process from state-$1$ to state-$2$,the pressure

The figure shows two flasks connected to each other. The volume of flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperatures $100\, K$ and $200\, K$ respectively. If the mass of the gas in flask $1$ is $m$,what is the mass of the gas in flask $2$?

An oxygen cylinder of volume $30 \; L$ has an initial gauge pressure of $15 \; atm$ and a temperature of $27 \; ^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \; atm$ and its temperature drops to $17 \; ^{\circ}C$. Estimate the mass (in $kg$) of oxygen taken out of the cylinder ($R = 8.31 \; J \; mol^{-1} K^{-1}$,molecular mass of $O_{2} = 32 \; u$).