(A) The ideal gas equation is given by $PV = \mu RT$,where $\mu = \frac{m}{M}$ is the number of moles.Substituting $\mu$,we get $PV = \frac{m}{M}RT$.S

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$\frac{P_1}{T_1 d_1} = \frac{P_2}{T_2 d_2}$

(A) The ideal gas equation is given by $PV = \mu RT$,where $\mu = \frac{m}{M}$ is the number of moles.Substituting $\mu$,we get $PV = \frac{m}{M}RT$.Since density $d = \frac{m}{V}$,we can write $V = \frac{m}{d}$.Substituting $V$ in the equation: $P(\frac{m}{d}) = \frac{m}{M}RT$.Simplifying,we get $P = \frac{d}{M}RT$,which implies $\frac{P}{dT} = \frac{R}{M} = \text{constant}$.Therefore,for two different states,we have $\frac{P_1}{d_1 T_1} = \frac{P_2}{d_2 T_2}$.

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

Medium

The equation of an ideal gas in terms of pressure $(P)$,absolute temperature $(T)$,and density $(d)$ is:

A
$\frac{P_1}{T_1 d_1} = \frac{P_2}{T_2 d_2}$
B
$\frac{P_1 T_1}{d_1} = \frac{P_2 T_2}{d_2}$
C
$\frac{P_1 d_2}{T_1} = \frac{P_2 d_1}{T_2}$
D
$\frac{P_1}{d_1 T_1} = \frac{P_2}{d_2 T_2}$

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

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?

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

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In the figure,the volume of container $X$ is twice the volume of container $Y$. Both contain an ideal gas. The temperature of $X$ is $200 \, K$ and the temperature of $Y$ is $400 \, K$. If the mass of the gas in $X$ is $m$,what will be the mass of the gas in $Y$?

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One mole of an ideal gas undergoes a process $P = \frac{2V^2}{1+V^2} \, Pa$. The change in temperature of the gas when the volume changes from $V = 1 \, m^3$ to $V = 2 \, m^3$ is:

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For one gram mole of a gas,the value of $R$ in the equation $PV = RT$ is nearly ...... $cal/K$

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The equation of an ideal gas in terms of pressure $(P)$,absolute temperature $(T)$,and density $(d)$ is:

Similar Questions

The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?

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

In the figure,the volume of container $X$ is twice the volume of container $Y$. Both contain an ideal gas. The temperature of $X$ is $200 \, K$ and the temperature of $Y$ is $400 \, K$. If the mass of the gas in $X$ is $m$,what will be the mass of the gas in $Y$?

One mole of an ideal gas undergoes a process $P = \frac{2V^2}{1+V^2} \, Pa$. The change in temperature of the gas when the volume changes from $V = 1 \, m^3$ to $V = 2 \, m^3$ is:

For one gram mole of a gas,the value of $R$ in the equation $PV = RT$ is nearly ...... $cal/K$

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