(II) An average active person consumes about 2500 Cal a day. (...

Question

(II) An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatt-hours? (c) If your power company charges about per kilowatt-hour, how much would your energy cost per day if you bought it from the power company? Could you feed yourself on this much money per day?

Accepted Answer

Hey, everyone in this problem, we're asked to consider the following scenario. So we have an electric heater that consumes 1500 joules of energy per second when operating. And there's two parts to this question. Part one, we're asked to find how many calories does it burn in an hour? And if the electricity is 12 cents per kilowatt hour, how much does it cost to run this heater continuously for a day? We're given four answer choices. Ok. So we kind of have two answers for each part of this question. So for part one, we have 1.29 multiplied by 10 to the exponent six calories or 3.58 multiplied by 10 to the exponent five calories. And for part two, we have $4.32 or $2.88. Ok. So two answers for each of the two parts. And that makes four possible answer choices when we do all of the combinations. Ok. We're gonna come back to those answer choices when we work through this problem. So let's start with part one. And what we're trying to find is the number of calories. It burns in an hour. Ok. We're given 1500 joules per second. So, calories per hour is just another way to measure this same thing. Ok. All right. So let's start. We have 1500 jewels per second and let's start by getting rid of the unit of jewel. Ok. We wanna convert that into calories. So we're gonna multiply by something with jewel in the denominator and recall that one calorie is equivalent to 4.186 Joules. So we multiply by one calorie divided by 4.186 Joules. The unit of Joules is gonna divide up and we're gonna be left with calories per second. All right. Now, we wanna convert that second into hours. So we're gonna multiply and we're gonna multiply by 60 seconds per minute and we know there are 60 seconds in every minute. That's gonna allow us to divide out that second and we're left with a unit of per minute. We're gonna do the same thing one more time because we know that there are 60 minutes per hour. Now, we can divide out that unit of minute and we're left with a unit of per hour, right. So we do all of these conversions and one thing at a time, just get you closer and closer to that answer. And now our units are in calories per hour, which is exactly what we want to find. So we have 1500 divided by 4.186 multiplied by 60 multiplied by 60. And if we work this all out, we have 1.29 multiplied by 10 to the exponent six calories per hour. All right. Let's take a look at our answer choices. So we have part one done. We found it to be 1.29 multiplied by 10 to the exponent six calories option A and B both have that answer as for part one, but C and D have 3.58 multiplied by 10 to the exponent five. So we can eliminate C and D. Now we're gonna move to part two in order to complete this question. So in part two, we wanna know how much it costs to run for a day. Ok. And we're told the cost per kilowatt hour. So if we have the cost per kilowatt hour, we need to know how many kilowatts we're dealing with. Well, let's recall that a watt W is equivalent to a jewel per second. So in the problem, we're told that this consumes 1500 jewels per second. That's 1500 jewels per second, which we can write as 1500 watts. Now, we mentioned this, we want this in kilowatts. So we have 1500 watts. We're gonna divide by 1000 to convert into kilowatts and we can write this as 1.5. Oops kilowatts. All right. Ok. So we know how many kilowatts we have per power. We know how many hours we have, let's go ahead and calculate this cost. Hm. So what we have is that it costs 12 cents, how kilowatt hour to run this thing? Ok. We know that we have 1.5 kilowatts and it takes 24 hours. Ok, an entire day is 24 hours. We multiply these three together, 0.12 multiplied by 1.5 multiplied by 24 hours. This is gonna give us $4.32. And that's the answer we were looking for that is gonna be the cost to run this heater continuously for a day. Go back to our answer choices. We had narrowed it down to option A or option B based on part one of the question. Now, we found that for part two, we have $4.32. And so the correct answer is going to be option A. Thanks everyone for watching. I hope this video helped see you in the next one.

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