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An inventor claims to have developed a power cycle capable of delivering a net work output of 400 kJ for an energy input by heat transfer of 1200 kJ. The system undergoing the cycle receives heat from a source of 550K and rejects heat to a sink of 350K. Determine if this is a valid claim.

Respuesta :

Answer: Valid claim

Explanation:

Given

Work output is [tex]W=400\ kJ[/tex]

Work input is [tex]Q=1200\ kJ[/tex]

The temperature of the source [tex]T_h=550\ K[/tex]

The temperature of the sink is [tex]T_l=350\ K[/tex]

Efficiency is given by

[tex]\eta =\dfrac{\text{W}}{\text{Q}}\times 100[/tex]

Insert the values

[tex]\Rightarrow \eta=\dfrac{400}{1200}\times 100\\\\\Rightarrow \eta=\dfrac{100}{3}\\\\\Rightarrow \eta=33.3\%[/tex]

For ideal cycle it is

[tex]\Rightarrow \eta=\dfrac{T_h-T_l}{T_l}\times 100\\\\\Rightarrow \eta=\dfrac{550-350}{550}\times 100\\\\\Rightarrow \eta=36.36\%[/tex]

The efficiency of the cycle is less than the ideal situation, therefore, it is valid claim.

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