Question

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.

Answer 1

Answer: Valid claim

Step-by-step explanation:

Given

Work output is
`W=400\ kJ`

Work input is
`Q=1200\ kJ`

The temperature of the source
`T_h=550\ K`

The temperature of the sink is
`T_l=350\ K`

Efficiency is given by

`\eta =\frac{\text{W}}{\text{Q}}* 100`

Insert the values

`\Rightarrow \eta=(400)/(1200)* 100\\\\\Rightarrow \eta=(100)/(3)\\\\\Rightarrow \eta=33.3\%`

For ideal cycle it is

`\Rightarrow \eta=(T_h-T_l)/(T_l)* 100\\\\\Rightarrow \eta=(550-350)/(550)* 100\\\\\Rightarrow \eta=36.36\%`

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