A 15 kW electric generator burns 1.2 gal of diesel fuel per hour. The energy density of diesel fuel is 140 MJ/gal. What is the generator's thermal efficiency?

Video transcript

Hey, everyone. So this problem is dealing with heat engines. Let's see what it's asking us. A 1200 watt portable power plant runs on liquid petroleum. The power plant consumes 0.5 liters of liquid petroleum per hour. The energy density per volume unit of this used liquid petroleum is 35 mega joules per liter. We're asked to calculate the thermal efficiency of this power plant. Our multiple choice answers are a 15% b 17% c 25% or D 34%. So the key to solving this problem is recalling the equation for efficiency, which is equal to our work divided by our total heat. And so because power is equal to work divided by time. If we look at this problem in a one second increment where our power is equal to 1200 watts, we can recall that a watt is equal to a jewels per second. Then our work is equal to 1200 jewels. And so we can go back to our efficiency given by Ada. And our work we've sold for is 1200 jewels divided by that total heat. So that's the next thing we need to find. And so our total heat, we're told that the energy density per volume. And so we can recall that, that rate oh fuel consumption, that what's given to us in the problem is 0.5 liters per hour. And so that's per 3600 seconds. And then we multiply that by our energy density which is 3. times 10 to the seven jewels per year, keeping everything in standard units. We're taking it from 35 mega joules to 3.7. So sorry, 3.5 times 10 to the seven Jews. And so then our rates uh she per time per unit time comes out to 4861 jewels per second. Again, because we are looking at this in a one second time frame, we can say our total heat is equal to 4861 jewels. And so then we plug that back into our original equation. 4860 one jewels plug that into our calculator and we get a thermal efficiency of 0.25 which is equal to 25%. And that aligns with answer choice C. That's all we have for this one. We'll see you in the next video.