Question

A very tall building has a height H0 on a cool spring day when the temperature is T0. You decide to 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 building is a length h taller than it was on the cool spring day where h is much much less than H0. Assume the entire frame of the building is made of steel, which has a coefficient of linear expansion αsteel.

Required:
What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?

Answer 1

Answer:

The temperature is   $T = \frac{h}{H_O \alpha_{steel} } + T_O$

Explanation:

From the question we are told that

      The height on a cool spring day is $H_O$

      The temperature on a cool spring day is  $T_O$

      The difference in height between a cool spring day and a summer day  is     h

     The coefficient of static friction is $\alpha _{steel}$

The mathematical relation for the linear expansion of the steel buiding is represented as

               $h = H_o \alpha_{steel} [T-T_O]$

Where T is the temperature of the steel during summer

Now making T the subject we have

                $T = \frac{h}{H_O \alpha_{steel} } + T_O$