A gas expands in a piston-cylinder device from V1 to V2- the process being described by P - aV - b- where P- Pressure and V- Volume- the work done in process is -

Given : P = aV + b Work done = ∫^V_2_V_1 PdV = ∫^V_2_V_1(aV+b)dV = ∫^V_2_V_1aVdV + ∫^V_2_V_1bdV = a[ln V]^V_2_V_1 + b [V]^V_2_V_1 =a[ln V_2 ln V_1] +b(V_2 V_1 ...

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Byju's Answer

Standard XII

Chemistry

Thermodynamic Processes

A gas expands...

Question

A gas expands in a piston-cylinder device from $V_{1}$ to $V_{2}$ , the process being described by $P = \frac{a}{V} + b$ , where P: Pressure and V: Volume, the work done in process is –

a l n \frac{V_{1}}{V_{2}} + b (V_{2} - V_{1})

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- a l n \frac{V_{2}}{V_{1}} - b (V_{2} - V_{1})

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- a l n \frac{V_{1}}{V_{2}} - b (V_{2} - V_{1})

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a l n \frac{V_{2}}{V_{1}} + b (V_{2} - V_{1})

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Solution

The correct option is D $a l n \frac{V_{2}}{V_{1}} + b (V_{2} - V_{1})$
Given : $P = \frac{a}{V} + b$
Work done $= \int_{V_{1}}^{V_{2}} P d V = \int_{V_{1}}^{V_{2}} (\frac{a}{V} + b) d V$
$= \int_{V_{1}}^{V_{2}} \frac{a}{V} d V + \int_{V_{1}}^{V_{2}} b d V = a [l n V]_{V_{1}}^{V_{2}} + b [V]_{V_{1}}^{V_{2}}$
$= a [l n V_{2} - l n V_{1}] + b (V_{2} - V_{1})$
$= a l n \frac{V_{2}}{V_{1}} + b (V_{2} - V_{1})$

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A gas expands in a piston-cylinder device from V1 to V2, the process being described by P=aV+b, where P: Pressure and V: Volume, the work done in process is –

The correct option is D a ln V2V1+b(V2−V1)Given : P=aV+b Work done =∫V2V1PdV=∫V2V1(aV+b)dV =∫V2V1aVdV+∫V2V1bdV=a[ln V]V2V1+b[V]V2V1 =a[ln V2−ln V1]+b(V2−V1) =a ln V2V1+b(V2−V1)

A gas expands in a piston-cylinder device from $V_{1}$ to $V_{2}$ , the process being described by $P = \frac{a}{V} + b$ , where P: Pressure and V: Volume, the work done in process is –