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Thermal Behavior of Matter and Heat Engines - Department of ...

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Answer:<br />

(a) In the dressing room:<br />

P<br />

net<br />

= eσA(<br />

T<br />

4<br />

− T<br />

4<br />

s<br />

= (0.900)[5.67 × 10<br />

)<br />

−8<br />

W /( m<br />

2<br />

⋅ K<br />

4<br />

2<br />

)](1.15m<br />

) × [(303 K)<br />

4<br />

− (293 K)<br />

4<br />

] = 62.1W<br />

(b)<br />

P<br />

net<br />

In the outdoor:<br />

= eσA(<br />

T<br />

4<br />

− T<br />

4<br />

s<br />

= (0.900)[5.67 × 10<br />

)<br />

−8<br />

W /( m<br />

2<br />

⋅ K<br />

4<br />

2<br />

)](1.15m<br />

) × [(303 K)<br />

4<br />

− (273 K)<br />

4<br />

] = 169W<br />

In the warm room the net radiated power is roughly that <strong>of</strong> a small lightbulb (about 60<br />

W); outdoors the net radiated power has more than doubled, <strong>and</strong> is comparable to that<br />

<strong>of</strong> a 150-W lightbulb.<br />

11.9 <strong>Heat</strong> engines <strong>and</strong> the Carnot cycle<br />

A heat engine is a device that converts heat into work. The classic example <strong>of</strong> this<br />

type <strong>of</strong> device is steam engine. The basic elements <strong>of</strong> a steam engine are a boiler,<br />

where heat converts water to steam, <strong>and</strong> a<br />

piston that can be displaced by the<br />

exp<strong>and</strong>ing steam. In some engines, the<br />

steam is simply exhausted into the<br />

atmosphere after it has exp<strong>and</strong>ed against<br />

the piston. More sophisticated engines<br />

send the exhaust steam to a condenser,<br />

where it is cooled <strong>and</strong> condensed back to<br />

liquid water, then recycled to the boiler.<br />

<strong>Heat</strong> engines have in common are:<br />

(i) A high temperature region, or reservoir,<br />

that supplies heat to the engine (the boiler<br />

in the steam engine);<br />

(ii) A low temperature reservoir where<br />

“waste” heat is released (the condenser in<br />

the steam engine); <strong>and</strong><br />

(iii) An engine that operates in a cycle fashion.<br />

16

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