Heat and Thermodynamics 5 Question 17
18. The shown $p$ - $V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is
(2013 Main)
(a) $p _0 V _0$
(b) $\left(\frac{13}{2}\right) p _0 V _0$
(c) $\left(\frac{11}{2}\right) p _0 V _0$
(d) $4 p _0 V _0$
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Solution:
- Heat is extracted from the source means heat is given to the system (or gas) or $Q$ is positive. This is positive only along the path $A B C$.
Heat supplied
$\therefore \quad Q _{A B C}=\Delta U _{A B C}+W _{A B C}$
$=n C _V\left(T _f-T _i\right)+$ Area under $p-V$ graph
$=n\left(\frac{3}{2} R\right)\left(T _C-T _A\right)+2 p _0 V _0$
$=\frac{3}{2}\left(n R T _C-n R T _A\right)+2 p _0 V _0$
$=\frac{3}{2}\left(p _C V _C-p _A V _A\right)+2 p _0 V _0$
$=\frac{3}{2}\left(4 p _0 V _0-p _0 V _0\right)+2 p _0 V _0=\frac{13}{2} p _0 V _0$
