A pressure P-absolute temperature T diagram w | vedclass

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(A) From the ideal gas equation,we have $PV = nRT$,which can be rewritten as $P = (nR/V)T$. Comparing this with the equation of a straight line passin

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(A) From the ideal gas equation,we have $PV = nRT$,which can be rewritten as $P = (nR/V)T$. Comparing this with the equation of a straight line passing through the origin,$y = mx$,where $y = P$ and $x = T$,the slope $m = nR/V$. In the given $P-T$ diagram,the line representing the process from state $1$ to state $2$ is a straight line that does not pass through the origin $(0,0)$. Let the equation of the line be $P = mT + c$,where $c > 0$ (since the intercept on the $P$-axis is positive). Substituting $P = nRT/V$,we get $nRT/V = mT + c$,or $V = nR / (m + c/T)$. As the temperature $T$ increases from state $1$ to state $2$,the term $c/T$ decreases. Consequently,the denominator $(m + c/T)$ decreases,which means the volume $V$ must increase.

$A$ pressure $P-$absolute temperature $T$ diagram was obtained when a given mass of gas was heated. During the heating process from state $1$ to state $2$,the volume:

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