QJEEM21Phdfe6: JEE Main 2021 Physics - Class 11 JEEM21Phdfe6 Solution: For an ideal gas the instantaneous change in pressure 'p' with…

Question

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For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation

{{dp} \over {dv}} = - ap

. If p = p₀ at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)

Accepted Answer

\int\limits_{{p_0}}^p {{{dp} \over P} = - a\int\limits_0^v {dv} }

\ln \left( {{p \over {{p_0}}}} \right) = - av

p = {p_0}{e^{ - av}}

For temperature maximum p-v product should be maximum

T = {{pv} \over {nR}} = {{{p_0}v{e^{ - av}}} \over R}

{{dT} \over {dv}} = 0 \Rightarrow {{{p_0}} \over R}\{ {e^{ - av}} + v{e^{ - av}}( - a)\}

= 0

{{{p_0}{e^{ - av}}} \over R}\{ 1 - av\} = 0

v = {1 \over a},\infty

T = {{{p_0}1} \over {Rae}} = {{{p_0}} \over {Rae}}

at v =

\infty

T = 0

Option (a)

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