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Question
A steam engine delivers 5.4×108 J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?
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Solution 1
Work done perminute, output =` 5.4 xx 10^8 J`
Heat absorbed per minute, input = `3.6 xx 10^9 J`
Efficiency, = eta = "output"/"input" = (5.4 xx 10^8)/(3.6 xx 10^9) = 0.15
`%eta = 0.15 xx 100 = 15`
Heat energy wasted /minute
= Heat energy absorbed / minute - Useful work done / minute
`= 3.6 xx 10^9 - 5.4 xx 10^8`
`= (3.6 - 0.54) xx 10^9 = 3.06 xx10^9 J`
Solution 2
Work done by the steam engine per minute, W = 5.4 × 108 J
Heat supplied from the boiler, H = 3.6 × 109 J
Efficiency of the engine = `"Output energy"/"Inut energy"`
`:.eta = W/H = (5.4 xx 10^8)/(3.6 xx 10^9) = 0.15`
Hence, the percentage efficiency of the engine is 15 %.
Amount of heat wasted = 3.6 × 109 – 5.4 × 108
= 30.6 × 108 = 3.06 × 109 J
Therefore, the amount of heat wasted per minute is 3.06 × 109 J.
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