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Standard XII

Physics

Real Gas Equation

he pressure p...

Question

he 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 when the temperature changes from $T_{1} t o T_{2}$ while the pressure remains constant, is given by.

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

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

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

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

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Solution

The correct option is D $A (T_{2} - T_{1}) - B (T_{2}^{2} - T_{1}^{2})$
ACCORDING TO THE QUESTION,
THE PRESSURE EXERTED BY THE GIVEN GAS IS GIVEN AS FOLLOWS:
$p = \frac{A T - B T^{2}}{v}$
AND FROM THE CONCEPT OF PRESSURE ENERGY AT GIVEN PRESSURE IS GIVEN BY:
$W = p d V$

SO FOR AT CONSTANT PRESSURE WE USE THE ABOVE FORMULA TO CALCULATE THE WORK DONE IN TERMS OF $v$ ,

$v = \frac{A T - B T^{2}}{p}$
PUTTING THIS VALUE IN ABOVE EQUATION:

$W = p [\frac{A T_{1} - B T_{1}^{2}}{p} - \frac{A T_{2} - B T_{2}^{2}}{p}]$

Or $W = (A T_{1} - B T_{1}^{2}) - (A T_{2} - B T_{2}^{2})$

HENCE THE OPTION (C) IS CORRECT.

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he 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 when the temperature changes from T1toT2 while the pressure remains constant, is given by.

he 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 when the temperature changes from $T_{1} t o T_{2}$ while the pressure remains constant, is given by.