One mole of a perfect gas in a cylinder fitted with a piston has a pressure $P,$ volume $V,$ and temperature $T.$ If the temperature is increased by $1 \, K$ keeping pressure constant,the increase in volume is

An ideal gas has an initial pressure of $3$ pressure units and an initial volume of $4$ volume units. The table gives the final pressure and volume of the gas (in those same units) in four processes. Which processes start and end on the same isotherm?

$A$. Process $A$	$P=5, V=7$
$B$. Process $B$	$P=4, V=6$
$C$. Process $C$	$P=12, V=1$
$D$. Process $D$	$P=6, V=3$

$A$ perfect gas at $27^{\circ}C$ is heated at constant pressure so as to double its volume. The final temperature of the gas will be,close to ...... $^{\circ}C$

Two identical glass bulbs are interconnected by a thin glass tube. Initially,both bulbs are at $0^{\circ}C$. $A$ gas is filled in these bulbs. When one bulb is placed in ice $(0^{\circ}C)$ and the other bulb is placed in a hot bath,the pressure of the gas becomes $1.5$ times the initial pressure. The temperature of the hot bath will be ...... $^{\circ}C$.

The number of air molecules in a $(5 \,m \times 5 \,m \times 4 \,m)$ room at standard temperature and pressure is of the order of

When $2 \, g$ of a gas are introduced into an evacuated flask kept at $25 \, ^\circ C$,the pressure is found to be $1 \, atm$. If $3 \, g$ of another gas is added to the same flask,the pressure becomes $1.5 \, atm$. The ratio of the molecular weights of these gases will be: