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PV Work

Pressure P, v...

Question

Pressure P, volume V and temperature T for a certain gas are related by $p = \frac{A T - B T^{2}}{V}$ , where A and B are constants.The work done by the gas as its temperature change from $T_{1}$ to $T_{2}$ while pressure remaining constant is:

A - \frac{B}{2} (T_{2} - T_{1}

)

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A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2}

)

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\frac{A}{2} T_{2}^{2} - T_{1}^{2}) - \frac{B}{3} (T_{2}^{3} - T_{1}^{3}

)

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A (T_{2} - T_{1})^{2} - \frac{B}{3} (T_{2} - T_{1})^{3}

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Solution

The correct option is B $A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2}$ )
$P =$ constant $\to$ Isobaric process
Work done $= P Δ V = n R Δ T$
$V = \frac{A T - {B T}^{2}}{P}$
$Δ V = \frac{1}{P} [A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2})]$
Work done $= P Δ V = P \times \frac{1}{P} \times [A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2})]$
$= A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2})$

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Pressure P, volume V and temperature T for a certain gas are related by p=AT−BT2V, where A and B are constants.The work done by the gas as its temperature change from T1 to T2 while pressure remaining constant is:

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Pressure P, volume V and temperature T for a certain gas are related by $p = \frac{A T - B T^{2}}{V}$ , where A and B are constants.The work done by the gas as its temperature change from $T_{1}$ to $T_{2}$ while pressure remaining constant is: