The $SI$ unit of universal gas constant is

State the Avogadro hypothesis.

The mass of oxygen gas occupying a volume of $11.2 \text{ litres}$ at a temperature $27^{\circ}C$ and a pressure of $760 \text{ mm}$ of mercury in kilograms is $[$ Molecular weight of oxygen $= 32]$

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

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P = P_0 \left[ 1 - \frac{1}{2} \left( \frac{V_0}{V} \right)^2 \right]$. Here $P_0$ and $V_0$ are constants. Calculate the change in the temperature of the gas if its volume changes from $V_0$ to $2V_0$.

$A$ gas of certain mass filled in a closed cylinder at a pressure of $3.23 \ kPa$ has a temperature of $50^{\circ} C$. The gas is now heated until its absolute temperature is doubled. The modified pressure is . . . . . . $Pa$.