An ideal gas system undergoes an isothermal process, then the work done during the process is

Question

An ideal gas system undergoes an isothermal process, then the work done during the process is (A)  nRT ln (V2/V1)  (B)  nRT ln (V1/V2)  (C)  2nRT ln (V2/V1)  (D)  2nRT ln ((V1/V2))

Tardigrade Admin · Accepted Answer

Let an ideal gas goes isothermally from its initial state

(P_{1} V_{1})

to the final state

(P_{2} V_{2})

, then work done

W = V_{1} \int V_{2} P d V

Taking

P V = n RT

or

P = \frac{n RT}{V}

Then,

W = V_{1} \int V_{2} \frac{n RT}{V} d V

= n RT V_{1} \int V_{2} \frac{d V}{V} = n RT l n \frac{V _{2}}{V _{1}}

Q. An ideal gas system undergoes an isothermal process, then the work done during the process is

$n RT l n \frac{V _{2}}{V _{1}}$

$n RT l n \frac{V _{1}}{V _{2}}$

$2 n RT l n \frac{V _{2}}{V _{1}}$

$2 n RT l n (\frac{V _{1}}{V _{2}})$

Q. An ideal gas system undergoes an isothermal process, then the work done during the process is

nRTlnV1​V2​​

nRTlnV2​V1​​

2nRTlnV1​V2​​

2nRTln(V2​V1​​)

Let an ideal gas goes isothermally from its initial state (P1​V1​) to the final state (P2​V2​) , then work done W=V1​∫V2​​PdV Taking PV=nRT or P=VnRT​ Then, W=V1​∫V2​​VnRT​dV =nRTV1​∫V2​​VdV​=nRTlnV1​V2​​

$n RT l n \frac{V _{2}}{V _{1}}$

$n RT l n \frac{V _{1}}{V _{2}}$

$2 n RT l n \frac{V _{2}}{V _{1}}$

$2 n RT l n (\frac{V _{1}}{V _{2}})$