A carnot heat engine uses a steam boiler at 100c as the high...

A Carnot heat engine uses a steam boiler at 100°C as the high-temperature reservoir. The low-temperature reservoir is the outside environment at 20.0°C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W. How much steam of power (in W) will it cause to condense in the high-temperature reservoir in 1.00 h?

Transcript

00:01 So let's say we have a carnot engine at a cold temperature, we're told, is 20 degrees celsius.

00:06 So this is 293 kelvin.

00:10 And it's got a high temperature of 100 degrees celsius.

00:16 And so this is 373 kelvin.

00:20 And we were told that energy is exhausted to the low temperature reservoir.

00:25 So the heat output is the derivative of.

00:30 Of this or the power output i should say is 15 .4 kilowatts or sorry 15 .4 watts and so we want to know given all this how much steam will condense in the due to the high temperature reservoir in a time interval of one hour so delta t will take to be 3 600 seconds okay so basically what we want to know is what mass of steam is can well will be condensed in this high temperature reservoir so first let's find the efficiency of our engine.

01:03 This is going to be 1 minus tc over t h.

01:07 So 1 minus 2 .93 over 373.

01:17 And so this is like 0 .214.

01:22 And that should be equal to the work divided by the heat input of the engine.

01:28 And the work is going to be the heat input.

01:34 Minus the heat output basically and we can rewrite this as the workout over basically the workout plus the heat output and we can just write these for like you know one second for instance so we can take the heat output per second is 15 .4 jules so this is equal to 0 .214 and so we have w is equal to w plus 15 .4 watts...

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