One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5°C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the Taipei 101 is 0.471 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?

Video transcript

Welcome back everybody. We are looking at a telecommunication tower and we are told that it has a height of 502 ft during its construction during the winter which at that time has a temperature of 13°C. Now we are told that it is made of steel and steel has an expansive itty constant of 1.2 times 10 to the negative 5°. They'll see us to -1. Now, when it turns to summer time, the tower is actually going to increase in height by 0.138 ft. And we are tasked with finding what the temperature of that summer weather is. Well, we know that the change in temperature is equal to well our final temperature minus our initial temperature equal to our change in height divided by our expansive. Itty constant times our initial height which rearranging some terms around here, we get that. Our final summer temperature then was our initial temperature plus our delta H. Divided by our expensive Itty constant times H. We know all these values. So let's just go ahead and plug them in. We have that our final temperature is equal to plus 0.138 divided by expansively constant of 1.2 times 10 to the negative five times +502. Which when you plug all this in your calculator, you get an answer of 35.9 degrees Celsius corresponding to our answer. Choice of thank you all so much for watching. Hope this video helped. We will see you all in the next one