The pressure ( P ) and temperature ( T ) rela | vedclass

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Question

$PT ^2=	ext { constant, Using } PV = nRT$

$P =\frac{ nRT }{ V } $

$ PT ^2=\frac{ nRT }{ V } 	imes T ^2=	ext { constant }$

$\Rightarrow T ^

Vedclass · Accepted Answer

$\frac{3}{T}$

Vedclass · Answer

$PT ^2=	ext { constant, Using } PV = nRT$

$P =\frac{ nRT }{ V } $

$ PT ^2=\frac{ nRT }{ V } 	imes T ^2=	ext { constant }$

$\Rightarrow T ^3= KV $

$	ext { So, } \frac{ d }{ dT }( KV )=3 T ^2$

$\Rightarrow \frac{ KdV }{ dT }=3 T ^2$

$\Rightarrow dV =\frac{3 T ^2}{ K } dT$

$dV = V \gamma dT \quad \Rightarrow \gamma=\frac{3 T ^2}{ KV ^2}=\frac{3 T ^2}{ T ^3}=\frac{3}{ T }$

$\Rightarrow \gamma V =\frac{3 T ^2}{ K }$

The pressure $( P )$ and temperature $( T )$ relationship of an ideal gas obeys the equation $PT ^2=$ constant. The volume expansion coefficient of the gas will be:

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