A certain gas is taken to the five states represented by dots in the graph- The plotted lines are isotherms- Order of the most probable speed v p of the molecules at these five states isA- V p at 3- V p at 1- V p at 2- V p at 4- V p at 5B- V p at 1- V p at 2- V p at 3- V p at 4- V p at 5C- V p at 3- V p at 2- V p at 4- V p at 1- V p at 5D- Insufficient information to predict the result-

The correct option is A V_p at 3 gt;V_p at 1=V_p at 2 gt;V_p at 4=V_p at 5The given p v graph represents three isotherms. For the uppermost isotherm, tempe ...

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Standard XII

Physics

Thermodynamic Processes

A certain gas...

Question

A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. Order of the most probable speed $v_{p}$ of the molecules at these five states is

V_{p a t 3} > V_{p a t 1} = V_{p a t 2} > V_{p a t 4} = V_{p a t 5}

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V_{p a t 1} > V_{p a t 2} = V_{p a t 3} > V_{p a t 4} = V_{p a t 5}

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V_{p a t 3} > V_{p a t 2} = V_{p a t 4} > V_{p a t 1} = V_{p a t 5}

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Insufficient information to predict the result.

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Solution

The correct option is A $V_{p a t 3} > V_{p a t 1} = V_{p a t 2} > V_{p a t 4} = V_{p a t 5}$
The given $p - v$ graph represents three isotherms.
For the uppermost isotherm, temperature will be highest.
$\Rightarrow T_{a} > T_{b} > T_{c}$

Points (1, 2) lie on isotherm b
$\Rightarrow T_{1} = T_{2} = T_{b}$
Points (4, 5) lie on on isotherm 'c'
$\Rightarrow T_{4} = T_{5} = T_{c}$
Hence order of temperature,
$T_{3} > T_{1} = T_{2} > T_{4} = T_{5}$
The most probable spead of gas molecules,
$v_{p} \propto \sqrt{T}$
$\Rightarrow V_{p_{3}} > V_{p_{1}} = V_{p_{2}} > V_{p_{4}} = V_{p_{5}}$

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A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. Order of the most probable speed vp of the molecules at these five states is

A certain gas is taken to the five states represented by dots in the graph. The plotted lines are isotherms. Order of the most probable speed $v_{p}$ of the molecules at these five states is