Expansion of an ideal gas of mass m at a constant pressure P is given by straight line D . Then expa

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12.Kinetic Theory of Gases

medium

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/ 2 $ is given by the straight line

$E$

$C$

$B$

$A$

Solution

ideal gas equation

$PV = nRT$

$n =\frac{ m }{ M }$

where

$m =$ weight in grams

$M =$ molecular weight

$PV =\frac{ m }{ M } RT$

$V =\left(\frac{ m }{ P }\right) \frac{ R }{ M } T$

slope of expansion curve is determined by $\left(\frac{m}{P}\right) \frac{R}{M}$

for mass $m$ and pressure $P$ slope

$S _{1}=\left(\frac{ m }{ P }\right) \frac{ R }{ M } \quad$ eq(1)

for mass $2 m$ and pressure $\frac{P}{2}$ slope

$S _{2}=\left(\frac{2 m }{\frac{ p }{2}}\right) \frac{ R }{ M }$

$S _{2}=4\left(\frac{ m }{ P }\right) \frac{ R }{ M } \quad eq (2)$

$\frac{e q(2)}{e q(1)}$

$S _{2}=4 S _{1}$

According to question given

$S _{1}=2$

$SO _{2}=8$

Standard 11

Physics

A cylinder containing gas at $27\,^oC$ is divided into two parts of equal volume each $100\,^oc$ and at equal pressure by a piston of cross sectional area $10.85\,\, cm^2$. The gas in one part is raised in temperature to $100\,^oC$ while the other maintained at original temperature. The piston and wall are perfect insulators. How far will the piston move during the change in temperature…. $cm$ .

normal

Two monoatomic ideal gas at temperature $T_1$ and $T_2$ are mixed. There is no loss of energy. If the masses of molecules of the two gases are $m_1$ and $m_2$ and number of their molecules are $n_1$ and $n_2$ respectively. The temperature of the mixture will be :

normal

A fix amount of nitrogen gas ($1$ mole) is taken and is subjected to pressure and temperature variation. The experiment is performed at high pressure as well as high temperatures. The results obtained are shown in the figures. The correct variation of $PV/RT$ with $P$ will be exhibited by

medium

One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$ . What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume

normal

A gas obeying the equation of state $p V=R T$ undergoes a hypothetical reversible process described by the equation, $p V^{5 / 3} \exp \left(-\frac{p V}{E_{0}}\right)=C_{1}$, where $C_{1}$ and $E_{0}$ are dimensioned constants. Then, for this process, the thermal compressibility at high temperature

normal

(KVPY-2017)

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/ 2 $ is given by the straight line

Solution

Similar Questions

Two monoatomic ideal gas at temperature $T_1$ and $T_2$ are mixed. There is no loss of energy. If the masses of molecules of the two gases are $m_1$ and $m_2$ and number of their molecules are $n_1$ and $n_2$ respectively. The temperature of the mixture will be :

A fix amount of nitrogen gas ($1$ mole) is taken and is subjected to pressure and temperature variation. The experiment is performed at high pressure as well as high temperatures. The results obtained are shown in the figures. The correct variation of $PV/RT$ with $P$ will be exhibited by

One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$ . What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume

A gas obeying the equation of state $p V=R T$ undergoes a hypothetical reversible process described by the equation, $p V^{5 / 3} \exp \left(-\frac{p V}{E_{0}}\right)=C_{1}$, where $C_{1}$ and $E_{0}$ are dimensioned constants. Then, for this process, the thermal compressibility at high temperature

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