A watt is a measure of power (the rate of energy change) equal to 1 J/s. (b) An adult person radiates heat to the surroundings at about the same rate as a 100-watt electric incandescent light bulb. What is the total amount of energy in kcal radiated to the surroundings by an adult over a 24 h period?

Video transcript

Hi everyone for this problem, we're told that a typical infrared light emits 175 watts of energy. We need to calculate the total energy emitted and kilocalories by the infrared lamp after 12 hours. And we're told that one watt is equal to one jewel per second. Okay, so we want to know how much light is emitted after 12 hours. So this is going to be our starting point. So 12 hours is our starting point and we want to know how much total energy is emitted. So we need to because we're told that one watt is jewels per second. We need to convert this hours to seconds. So let's start there. So in one hour we have minutes And in one minute we have 60 seconds. Okay, so let's just make sure we're in seconds now instead of ours, our hours cancel, our minutes cancel and we're in seconds. Perfect. So we also are told that we have watts of energy and one watt is equal to one jewel per second. So this 175 watts of energy is essentially 175 jewels per second. Okay, that's what that translates to. So we can go ahead and plug that into our calculation here as a conversion. So There's 175 jewels per second. That's what a typical infrared light emits. Okay, so now our seconds cancel and we're in jewels. The question asked us to calculate the total energy emitted and kilocalories so we need to know, what is that conversion from jewels to kill a calorie. And that conversion is In one killer Calorie. There is 4. Times 10 to the three jewels. So we're going to need to know that. So when we plug that in one kill a calorie Over 4.18, 4 times 10 to the three jewels. Now our jewels cancel and we're left with the unit of kilocalories, which is what we're looking for. So let's go ahead and solve and do the math here. And when we do, we get a final answer of 1.8 times 10 to the three kill a calorie. And this is going to be our final answer. This is the total Energy emitted and kilocalories by the infrared lamp. After 12 hours, I hope this was helpful.