If $\alpha$ and $\beta$ are the volume and pressure coefficients respectively of an ideal gas, then

Two containers $C_{1}$ and $C_{2}$ of volumes $V$ and $4V$ respectively,hold the same ideal gas and are connected by a thin horizontal tube of negligible volume with a valve which is initially closed. The initial pressures of the gas in $C_{1}$ and $C_{2}$ are $p$ and $5p$,respectively. Heat baths are employed to maintain the temperatures in the containers at $300 \, K$ and $400 \, K$,respectively. The valve is now opened. Select the correct statement.

$A$ monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. Given $\frac{V_2}{V_1} = 2$ and $\frac{V_4}{V_1} = 4$. The temperature at state $1$ is $T_1 = 27\,^oC$. Find the temperature at state $2$,i.e.,$T_2$ in $K$.

At the same temperature,pressure,and volume of two gases,which of the following quantities is constant?

$A$ hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$,hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first set in? (in $K$)

An ideal gas has pressure $P$,volume $V$ and absolute temperature $T$. If $m$ is the mass of each molecule and $K$ is the Boltzmann constant,then the density of the gas is: