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Natasha2012
2 months ago
10

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 o

f 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?
Physics
1 answer:
ValentinkaMS [3.4K]2 months ago
5 0

Response:

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

Justification:

According to the information provided in the question,

The height on a cool spring day measures H_O

The temperature for a cool spring day registers as T_O

The height variation between a cool spring day and a summer day is accounted as h

The static friction coefficient stands at \alpha _{steel}

The equation outlining the linear expansion for the steel building is given as

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

In this case, T represents the steel's temperature during summer

Rearranging for T, we derive

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

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