A power plant working on Carnot cycle has heat addition at $1000^{\circ} C$ and the cycle is repeated 1100 times per minute. The compression ratio is 10. The work produced is 475 kW.

The amount of heat supplied per cycle is ____ kJ/cycle.

43.04

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Solution

The correct option is A 43.04

$T_{1} = T_{2} {(\frac{v_{2}}{v_{1}})}^{y - 1}$

$= 1273 {(\frac{1}{10})}^{0.1} = 506.80 K$

$η_{C a r n o t} = 1 - \frac{T_{1}}{T_{2}} = 1 - \frac{506.80}{1273} = 0.60189$

$W_{c y c l e} = \frac{W_{n e t}}{N} = \frac{475 \times 60}{1100} = 25.9 k J / c y c l e$

$∴ η_{C a r n o t} = \frac{(W_{c y c l e}}{Q_{i n}}$
$\Rightarrow Q_{i n} = \frac{25.9}{0.60189} = 43.04 k J / C y c l e$

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A power plant working on Carnot cycle has heat addition at 1000∘C and the cycle is repeated 1100 times per minute. The compression ratio is 10. The work produced is 475 kW. The amount of heat supplied per cycle is ____ kJ/cycle. 43.04

The correct option is A 43.04 T1=T2(v2v1)y−1 =1273(110)0.1=506.80 K ηCarnot=1−T1T2=1−506.801273=0.60189 Wcycle=WnetN=475×601100=25.9 kJ/cycle ∴ηCarnot=(WcycleQin ⇒Qin=25.90.60189=43.04 kJ/Cycle

A power plant working on Carnot cycle has heat addition at $1000^{\circ} C$ and the cycle is repeated 1100 times per minute. The compression ratio is 10. The work produced is 475 kW.

The amount of heat supplied per cycle is ____ kJ/cycle.

43.04