> Q. The pressure $p$, volume $V$ and temperature $T$ for a certain gas are related by $p = frac{AT-BT^{2}}{v},$ where $A$ and $B$ are constants. The work done by the gas when the temperature changes from $T_1$ to $T_2$ while the pressure remains constant, is given by – LIVE ANSWER TODAY

Q. The pressure $p$, volume $V$ and temperature $T$ for a certain gas are related by $p = frac{AT-BT^{2}}{v},$ where $A$ and $B$ are constants. The work done by the gas when the temperature changes from $T_1$ to $T_2$ while the pressure remains constant, is given by

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The pressure $p$, volume $V$ and temperature $T$ for a certain gas are related by $p = frac{AT-BT^{2}}{v},$ where $A$ and $B$ are constants. The work done by the gas when the temperature changes from $T_1$ to $T_2$ while the pressure remains constant, is given by

Solution:

$v = frac{AT-BT^{2}}{p}$

$W = pDelta v = pleft[v_{2}-v_{1}right]$

$= pleft[frac{AT_{2}-BT^{2}_{2}}{p}-left(frac{AT_{1}-BT_{1}^{2}}{p}right)right]$

$= left[Aleft(T_{2}-T_{1}right)-Bleft(T^{2}_{2}-T^{2}_{1}right)right]$

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