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

The temperature is
`T = (h)/(H_O \alpha_(steel) ) + T_O`

Step-by-step 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 = (h)/(H_O \alpha_(steel) ) + T_O`