An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?

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An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?

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Answer 1 · 2018-03-02T02:04:21

$T V^{\frac{1}{3}} = constant$ $TV^{1/3} = \mbox{ constant}$

Explanation:

For an infinitesimal process
$d U = \frac{3}{2} n R d T = δ Q - p d V = δ Q - \frac{δ Q}{2} = \frac{δ Q}{2} = \frac{1}{2} p d V$ $dU = 3/2 nRdT = delta Q-pdV = delta Q-{deltaQ}/2 = {delta Q}/2=1/2pdV$

Using $p V = n R T$ $pV = nRT$ , this can be rewritten as

$\frac{3}{2} n R d T = \frac{1}{2} \frac{n R T}{V} d V \Rightarrow \frac{d T}{T} = \frac{1}{3} \frac{d V}{V} \Rightarrow$ $3/2 nR dT = 1/2 {nRT}/V dV implies {dT}/T = 1/3 {dV}/V implies$

$T V^{\frac{1}{3}} = constant$ $TV^{1/3} = \mbox{ constant}$

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An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?

1 Answer

Explanation:

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