An open vessel at $27\,^oC$ is heated such that $\frac{3}{5}$ of the air in it is expelled. Assuming the volume of the vessel remains constant,calculate the temperature in $K$ to which the vessel was heated.

At $T \ (K)$ for one mole of an ideal gas,the graph of $P$ (on $y$-axis) and $V^{-1}$ (on $x$-axis) gave a straight line with a slope of $32.8 \ L \ atm \ mol^{-1}$. What is the temperature (in $K$)? $\left(R=0.082 \ L \ atm \ K^{-1} \ mol^{-1}\right)$

$A$ $5.75 \ g$ sample of a gas occupies $3.5 \ L$ at $55 \ ^oC$ and $0.940 \ atm$ pressure. What is the molecular weight of the gas?

Explain the relationship between the moles of a gas,its volume,and its density.

If the density of a gas at sea level is $1.5 \ mg \ L^{-1}$,find the density of that gas on Mount Abu,where the pressure is $0.5 \ bar$. (Assume pressure at sea level is $1.0 \ bar$ and use the formula $\frac{d_1}{d_2} = \frac{p_1}{p_2}$) (in $mg \ L^{-1}$)

Which of the following represents the correct relationship between the change in density of an ideal gas and the change in temperature?