Question

One mole of Helium gas undergoes a reversible cyclic process ABCDA as shown in the figure.
Assuming gas to the ideal, answer the following questions:

What is the value of ‘q’ for the overall cyclic process?

• A. $-100\text{R ln 2}$
• B. $+100\text{R ln 2}$
• C. $+200\text{R ln 2}$
• D. $-200\text{R ln 2}$

Answer 1

Answer: (B)

$+100\text{R ln 2}$

AB, CD : isothermal; BC, DA : isobaric.
$\therefore q_{AB}=-{\omega }_{AB}=1\times R\times 300ln\left(\frac{1}{2}\right)=-300Rln2$
[as,$\omega =-nRTln\left(\frac{P_1}{P_2}\right)$]
$q_{BC}=n{C}_P△T=1\times \frac{5}{2}R\times 100=250R$
$q_{CD}=-{\omega }_{CD}=1\times R\times 400ln\left(2/1\right)=400Rln2$
$q_{DA}=n{C}_p△T=1\times \frac{5}{2}R\times -100=250R$
$\therefore q_{total}=100Rln2$