The power output of a car engine running at 2400 rpm is 500 kW. How much (a) work is done and (b) heat is exhausted per cycle if the engine's thermal efficiency is 20%? Give your answers in kJ.

Question

Accepted Answer

Hey, everyone. So this problem is dealing with heat engines. Let's see what it's asking us. We have a motorcycle that has an engine with an output power of horsepower and a rotational speed of revolutions per minute. Assuming that the engine operates in a closed cycle and has a thermal efficiency of 25%. We're asked to calculate the engine's work and the heat output in one cycle. Our multiple choice answers in units of jewels are a 187 and 561 B 187 and C 225 or D 220 1120. So the first step to solving this problem is recalling our thermal efficiency equation which is a is equal to the work divided by the total heat. Now, we are not given the work, but we are given the horse power. And so we can recall that power is equal to work divided by time. And so we can solve for our work using that equation. So that work is going to be, is going to be equal to power multiplied by time. And so our power listed is horsepower. And we can recall that the conversion between watts and horsepower to keep everything in standard units is 746 watts per horsepower. Then multiplied by the time we were looking for the time in one cycle. And so with the rotational speed of 3600 revolutions per minute, that means in one second, we'll have 60 cycles. And so we need to make sure that we are looking at just one cycle, so we'll divide by 60. And so then we plug that into our calculator and we get a work of 187 jewels. And so that was step one and looking at our multiple choice answers, we can immediately eliminate answer choices C and D. Now we're asked to calculate that heat outputs that total heat. And we were given thermal efficiency we saw for work. So now we can rearrange this equation to isolate heat Q on the left-hand side. And that will be Q is equal to our work divided by data or efficiency. And so then we plug in those values work we just saw for 187 jewels divided by our efficiency of 25% or 0.25 plug that in to our calculator and we get 748 jewels. Now, the last step they're asking for is So the last, what they're asking for is our heat output. And so the last step is recalling that our total heat is equal to the work plus our exhaust heat or our heat output. And so QE is equal to our Q total minus our work. So 700 sorry, 48 jewels minus 187 Jews gives us 561 jewels. And so that is the final answer for our heat output or heat or exhaust heat in one cycle. So that aligns with answer choice. A so that's all we have for this one. We'll see you in the next video.

The power output of a car engine running at 2400 rpm is 500 kW. How much (a) work is done and (b) heat is exhausted per cycle if the engine's thermal efficiency is 20%? Give your answers in kJ.

Verified Solution

Key Concepts

Power and Work

Thermal Efficiency

Heat Exhaust