12.7 A steam engine delivers 5.4×108J of work per minute and services 3.6 × 109J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?
Work done by the steam engine per minute, W = 5.4 J
Heat supplied by the boiler, H = 3.6 J
Efficiency of the engine, = = = 0.15
Amount of heat wasted = Input energy – Output energy
= 3.6 5.4 J
<p>Work done by the steam engine per minute, W = 5.4 <span title="Click to copy mathml"><math><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>8</mn></mrow></mrow></msup></math></span> J</p><p>Heat supplied by the boiler, H = 3.6 <span title="Click to copy mathml"><math><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>9</mn></mrow></mrow></msup></math></span> J</p><p>Efficiency of the engine, <span title="Click to copy mathml"><math><mi>η</mi></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>O</mi><mi>u</mi><mi>t</mi><mi>p</mi><mi>u</mi><mi>t</mi><mi></mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>y</mi></mrow></mrow><mrow><mrow><mi>I</mi><mi>n</mi><mi>p</mi><mi>u</mi><mi>t</mi><mi></mi><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>y</mi></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>5.4</mn><mi mathvariant="normal"></mi><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>8</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>3.6</mn><mi mathvariant="normal"></mi><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>9</mn></mrow></mrow></msup></mrow></mrow></mfrac></math></span> = 0.15</p><p>Amount of heat wasted = Input energy – Output energy</p><p>= 3.6 <span title="Click to copy mathml"><math><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>9</mn></mrow></mrow></msup><mo>-</mo><mi></mi></math></span> 5.4 <span title="Click to copy mathml"><math><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>8</mn></mrow></mrow></msup><mo>=</mo><mn>3.06</mn><mi></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>9</mn></mrow></mrow></msup></math></span> J</p>
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