Question

Two moles of helium gas undergo a cyclic process as shown in figure. Assuming the gs to be ideal, calculate the following quantities in this process. The net work done in $J$.

Answer 1

Using the ideal gas equation, we figure the states for each state.

• A -> $2atm,300K,0.025m^{-3}$
• B -> $2atm,400K,0.033m^{-3}$
• C -> $1atm,400K,0.0665m^{-3}$
• D -> $1atm,300K,0.050m^{-3}$
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And the transitions along with their individual work done:

• A -> B (isobaric); $w=P(V_B-V_A)=-1.6\times {10}^{3}J$
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• B -> C (isothermal); $w=nRTln\left(\frac{V_C}{V_B}\right)=4.66\times {10}^{3}J$
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• C -> D (isobaric); $w=P(V_D-V_C)=-1.650\times {10}^{3}J$
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• D -> A (isothermal); $w=nRT\ln \left(\frac{V_D}{V_A}\right)=3.457\times {10}^{3}J$
• 
  

Net Work done = $4867J$