Pressure of an ideal gas,contained in a closed vessel,is increased by $0.4 \%$ when heated by $1^{\circ} C$. Its initial temperature must be

The figure shows graphs of pressure $(P)$ versus density $(\rho)$ for an ideal gas at two temperatures $T_1$ and $T_2$.

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 $D$	$P=6, V=3$

There are two vessels filled with an ideal gas where the volume of one is double the volume of the other. The large vessel contains the gas at $8 \ kPa$ at $1000 \ K$,while the smaller vessel contains the gas at $7 \ kPa$ at $500 \ K$. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at $600 \ K$,at steady state the pressure in the vessels will be (in $kPa$).

One mole of an ideal gas undergoes a process in which pressure $P$ varies with volume $V$ as $P = 3 - g \left(\frac{V}{V_0}\right)^2$, where $V_0$ and $g$ are constants. The maximum temperature attainable by the ideal gas during this process is ($All$ quantities are in $SI$ units and $R$ is the gas constant).

If in a given container there is a gas of mass $M$ and $M_{0}$ is its molar mass,then what will be the number of moles?