The temperature of a gas having $2.0 \times 10^{25}$ molecules per cubic meter at $1.38 \text{ atm}$ (Given,$k = 1.38 \times 10^{-23} \text{ J K}^{-1}$) is: (in $\text{ K}$)

Which of the following shows the correct relationship between the pressure $P$ and density $\rho$ of an ideal gas at constant temperature?

$A$ cylindrical tube of cross-sectional area $A$ has two airtight,frictionless pistons at its two ends. The pistons are tied with a straight piece of metallic wire. The tube contains a gas at atmospheric pressure $P_0$ and temperature $T_0$. If the temperature of the gas is doubled,then the tension in the wire is:

What is the nature of the $P$ versus $1/V$ graph at a constant temperature?

$A$ balloon contains $1500 \ m^3$ of $He$ at $27^{\circ} C$ and $4 \ atm$ pressure. The volume of $He$ at $-3^{\circ} C$ temperature and $2 \ atm$ pressure will be: (in $m^3$)

Hydrogen gas and oxygen gas have a volume of $1 \, cm^3$ each at $N.T.P$. Which of the following statements is correct?