(D) According to the ideal gas equation:$P V = n R T$Since the volume $V$ is constant for each vessel,we can write:$P = \left( \frac{n R}{V} \right) T

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(D) According to the ideal gas equation:$P V = n R T$Since the volume $V$ is constant for each vessel,we can write:$P = \left( \frac{n R}{V} \right) T$This equation is of the form $y = m x$,where $y = P$,$x = T$,and the slope $m = \frac{n R}{V}$.Since the mass is given,$n$ is constant. However,the volumes $V$ of the small and large vessels are different.Therefore,the slope $m = \frac{n R}{V}$ will be different for the two vessels.Thus,the $P-T$ curves are linear,passing through the origin,but with different slopes.

Class 11 Physics Kinetic Theory of Gases Gas Laws (Charles, Boyle's, Avagadro's, Gay Lussacs and Dalton's law) and Ideal gas Equation

Medium

$A$ perfect gas of a given mass is heated first in a small vessel and then in a large vessel,such that their volumes remain unchanged. The $P-T$ curves are

A
parabolic with same curvature
B
parabolic with different curvature
C
linear with same slopes
D
linear with different slopes

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Class 11

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Kinetic Theory of Gases

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Gas Laws (Charles, Boyle's, Avagadro's, Gay Lussacs and Dalton's law) and Ideal gas Equation

An electron tube was sealed off during manufacture at a pressure of $1.2 \times 10^{-7} \text{ mm}$ of mercury at $27^{\circ}C$. Its volume is $100 \text{ cm}^3$. The number of molecules that remain in the tube is

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At $100 \, K$ and $0.1 \, \text{atm}$ pressure, the volume of helium gas is $10 \, \text{litres}$. If volume and pressure are doubled, its temperature will change to ....... $K$.

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The equation of state for $5 \ g$ of oxygen gas at pressure $P$,volume $V$,and temperature $T$ is given by:

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$A$ balloon contains $1500 \, m^3$ of helium at $27^\circ C$ and $4 \, atm$ pressure. The volume of helium at $-3^\circ C$ temperature and $2 \, atm$ pressure will be ...... $m^3$.

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The temperature of a gas contained in a closed vessel of constant volume increases by $1^{\circ} C$ when the pressure of the gas is increased by $1 \%$. The initial temperature of the gas is

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$A$ perfect gas of a given mass is heated first in a small vessel and then in a large vessel,such that their volumes remain unchanged. The $P-T$ curves are

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An electron tube was sealed off during manufacture at a pressure of $1.2 \times 10^{-7} \text{ mm}$ of mercury at $27^{\circ}C$. Its volume is $100 \text{ cm}^3$. The number of molecules that remain in the tube is

At $100 \, K$ and $0.1 \, \text{atm}$ pressure, the volume of helium gas is $10 \, \text{litres}$. If volume and pressure are doubled, its temperature will change to ....... $K$.

The equation of state for $5 \ g$ of oxygen gas at pressure $P$,volume $V$,and temperature $T$ is given by:

$A$ balloon contains $1500 \, m^3$ of helium at $27^\circ C$ and $4 \, atm$ pressure. The volume of helium at $-3^\circ C$ temperature and $2 \, atm$ pressure will be ...... $m^3$.

The temperature of a gas contained in a closed vessel of constant volume increases by $1^{\circ} C$ when the pressure of the gas is increased by $1 \%$. The initial temperature of the gas is

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