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Thermodynamics Part 1

Section: Physics

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Question : 53 of 100

Marks: +1, -0

Helium gas goes through a cycle

A B C D

(consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

$15.4 \%$
$9.1 \%$
$10.5 \%$
$12.5 \%$

Solution:

Heat given to system

= (n C_v \Delta T)_{A \rightarrow B} + (n C_p \Delta T)_{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 B} \rightarrow

\; = \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]_{B \rightarrow C}

\; = \; \frac{13}{2} P_0 V_0

\; \; \text{ and } \; W_0 = P_0 V_0

\; \eta = \; \frac{ \; \text{ Work } \; }{ \; \text{ heat given } \; }

\; = \; \frac{P_0 V_0}{ \frac{18}{2} P_0 V_0 } \times 100

\; = 15.4 \%

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