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Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as two years.) Suppose you wish to install the extra insulation in Exercise $14.41 .$ If energy cost $\$ 1.00$ per million joules and the insulation was $\$ 4.00$ per square meter, then calculate the simple payback time. Take the average $\Delta T$ for the 120 day heating season to be $15.0^{\circ}{C}$

The payback period is 32 days.

Physics 101 Mechanics

Chapter 14

Heat and Heat Transfer Methods

Thermal Properties of Matter

Simon Fraser University

University of Sheffield

University of Winnipeg

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Let's first remember what we know from, ah question for 21 from Question 40 when we know that Q two divided by Cuban, is equal to 0.65 So if you two is point so there is a 35% saving in hitting. Now let's first find out what's the area off houses. Area off house from Question 41 again is found by the dimensions given to us Waas chained across 15 plus three. So area will have so assume that it's a rectangular cube, not to Square Cube, but rectangle okay with me is that let's say this is 10 15 and then there is this side, which is just three. So we have six such surfaces. One surface has a dimension off. 10 cross 15 which is front one. This office has 15 close three on one more surface, which is this 10 crossed three. But there are six offices so twice there, so you can solve this 1 50 just 45 that's 1 95 less 31 95 plus thirties to 25 to 25 times two will be 4 15 So that's the area on which we will be will be installing the insulation. Now. Next part is to find out key one by t Hey, as we know it is given by K times eight times Delta T. The change in temperature divided by the thickness now value of K is 0.42 Area, as we found before, is 4 15 and change in temperature is 15. We can keep it in degrees or Kelvin doesn't matter, because this is a change in temperature or difference in the temperature and the thickness is 0.15 So, people from this calculation you'll find that value is 18 90 Jules for a second since this term and this time give you 100 and uh, 40 times 40 1600. We can simply you plan simply just by doing mental calculation verify this that it is indeed 18 90 Jews per second. From this, you can find que tu on using you to back. Human is equal to 0.65 You can divide numerator and denominator. Bye t. Then you have Q two divided by t on cue one divided by T, which is yet equal 2.65 Now you two divided by tea will be he one divided by tee times, points expired. So Cuban, divided by t, is 18 90. If you multiply by 0.65 you'll get 12 29 Jules per seconds. Now. From this, it's now we can find that. What's the difference between this and the Cuban bitey? So let's find the difference in the hit. The Unit Time, which is equal to 18 90 minus 2029 equals 6 62 juice for sickens, so we'll be saving 6 62 jewels for seconds. So let's convert it per hour. Let's see how much we save for our now to do that. All we have to do is 6 62 since it is juice. Four seconds and one hour contained 3600 seconds. So seconds divided by our it's one hour, which is equal to 2.38 million. So Jules per hour. So we'll be saving 2.38 million Jews per hour. And since the question say's we are saving $1 per 1,000,000 Jews, it means that we'll be saving 2.38 dollars. Our now let's first find out. Let's also find out area off installation on whole surface. Since we are given that it's $4 per square meter and we have 4 50 square meters, this will be 1800 dollars as a net. Then payback period will be just so idiot is equal to 1800. So we have to get back all the $1800 and we know that we're saving 2.38 dot per hour. So let's find out how many hours will need to make 1800 back. So 1800 divided by 2.38 It's 7 56 point see hours, so to convert, let's convert it in two days. One day is 24 hours, so if you just divided by 24 again, you'll find that it's 31.5 days or approximately 32 days. So the payback period is 32 days.

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