If the volume of gas is changed from V1 to V2 isothermally, then work done is:

Question

If the volume of gas is changed from V1 to V2 isothermally, then work done is: (A)  RT ln (V1/V2)  (B)  RT ln (V2/V1)  (C)  R(T2-T1) ln(V2/V1)  (D)  R(V2-V1) ln(T2/T1)

Tardigrade Admin · Accepted Answer

Ideal gas equation is PV=RT Work done in isothermal process is W=∫ limitsV1V2p dV From ideal gas law PV=RT ∴ W=∫ limitsV1V2( (RT/V) ) dV=RT∫ limitsV1V2(dV/V) ⇒ W=RT ln ( (V2/V1) )

Q. If the volume of gas is changed from $V_{1}$ to $V_{2}$ isothermally, then work done is:

$RT ln \frac{V _{1}}{V _{2}}$

$RT ln \frac{V _{2}}{V _{1}}$

$R (T_{2} - T_{1}) ln \frac{V _{2}}{V _{1}}$

$R (V_{2} - V_{1}) ln \frac{T _{2}}{T _{1}}$

Ideal gas equation is $P V = RT$
Work done in isothermal process is
$W = V_{1} \int V_{2} p d V$
From ideal gas law $P V = RT$
$∴$ $W = V_{1} \int V_{2} (\frac{RT}{V}) d V = RT V_{1} \int V_{2} \frac{d V}{V}$
$\Rightarrow W = RT ln (\frac{V _{2}}{V _{1}})$

Q. If the volume of gas is changed from V1​ to V2​ isothermally, then work done is:

RTlnV2​V1​​

RTlnV1​V2​​

R(T2​−T1​)lnV1​V2​​

R(V2​−V1​)lnT1​T2​​