Question 562: Thermodynamics & KTG

Question

An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The
percentage efficiency of the engine is close to __________.

Accepted Answer

% efficiency of carnot engine $$\eta $$ = $${W \over {{Q_{in}}}} 	imes 100$$
Work = Area of ABCD = (2P
0
)(V
0
)
Q
in
= Q
AB
+ Q
BC
Q
AB
= isochoric process
= nC
V
(T
B
- T
A
)
= 1 $$ 	imes $$ $${3 \over 2}R\left( {{T_B} - {T_A}} ight)$$
= $${3 \over 2}R\left( {{{3{P_0}{V_0}} \over R} - {{{P_0}{V_0}} \over R}} ight)$$
= 3P
0
V
0
Q
BC
= isobaric process
= nC
P
$$\Delta $$T
= $$1 	imes {5 \over 2}R$$(T
C
- T
B
)
= $${5 \over 2}R\left( {{{6{P_0}{V_0}} \over R} - {{3{P_0}{V_0}} \over R}} ight)$$
= 7.5 P
0
V
0
$$ 	herefore $$ $$\eta $$ = $${{{2{P_0}{V_0}} \over {3{P_0}{V_0} + 7.5{P_0}{V_0}}}}$$ $$ 	imes $$ 100
$$ \simeq $$ 19%

Thermodynamics & KTG

An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.

Integer / Numeric Answer Type