Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown

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11.Thermodynamics

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Helium gas goes through a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly ..... $\%$ (Assume the gas to be close to ideal gas)

A

$12.5$

B

$15.4$

C

$9.1$

D

$10.5$

Solution

Heat given to system $=\left(n C_{V} \Delta T\right)_{A \rightarrow B}+\left(b C_{P} \Delta T\right)_{B \rightarrow C}$

$=\left[\frac{3}{2}(n R \Delta T)\right]_{A \rightarrow B}+\left[\frac{5}{2}(n R \Delta T)\right]_{B, \rightarrow C}$

$\left[\frac{3}{2} \times V_{0} \Delta P\right]_{A \rightarrow B}+\left[\frac{5}{2} \times 2 P_{0} \times V_{0}\right]$

$=\frac{13}{2} P_{0} V_{0}$

and $W_{0}=P_{0} V_{0}$

$\eta=W$ or $\frac{k}{\text { heatgiven }}=\frac{P-0 V_{0}}{\frac{13}{2} P_{0} V_{0}} \times 100=15.4 \%$

Standard 11

Physics

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