Question

Calculate the work WC done by the gas during the isothermal expansion. Express WC in terms of p0, V0, and Rv.

Answer 1

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The expression is  $W_c = P_o V_o ln (R_v)$  

Explanation:

Generally smallest workdone done by  a gas is mathematically represented as

          $dW = PdV$

Generally for an isothermal process

    $PV = nRT = constant$

=>   $P = \frac{nRT}{V}$

Generally the total workdone is mathematically represented as

   $W_c = \int\limits^{v_f}_{V_o} {\frac{nRT}{V} } \, dV$

=> $W_c = nRT \int\limits^{V_f}_{V_o} {\frac{1}{V} } \, dV$

=>  $nRT [lnV] | \left \ {V_f}} \atop {V_o}} \right.$

=>  $W_c = nRT [ln(V_f) - ln(V_o)]$

=>  $W_c = nRT ln \frac{V_f}{V_o}$

From the question $\frac{V_f}{V_o } = R_v$

=> $W_c = P Vln (R_v)$

at initial  state

$W_c = P_o V_o ln (R_v)$