Above P-V diagram represents thermodynamic cycle of an engine, operating with an ideal monatomic gas

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11.Thermodynamics

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The above $P-V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

A

$4P_0V_0$

B

$P_0V_0$

C

$\left( {\frac{{13}}{2}} \right)$ $ P_0V_0$

D

$\;\left( {\frac{{11}}{2}} \right)$ $ P_0V_0$

(JEE MAIN-2013)

Solution

$Heat\,given\,to\,system = {\left( {n{C_V}\Delta T} \right)_{A \to B}} + {\left( {n{C_P}\Delta T} \right)_{B \to C}}$

$ = {\left[ {\frac{3}{2}\left( {nR\Delta T} \right)} \right]_{A \to B}} + {\left[ {\frac{5}{2}\left( {nR\Delta T} \right)} \right]_{B \to C}}$

$ = {\left[ {\frac{3}{2} \times {V_0}\Delta P} \right]_{A \to B}} + \left[ {\frac{5}{2} \times 2{P_0} \times {V_0}} \right]$

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

Standard 11

Physics

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