The Eiffel Tower is a steel structure whose height increases by 19.7 cm when the temperature changes from -9 to +40 oC. What is the approximate height (in meters) at the lower temperature?
To find the approximate height of the Eiffel Tower at the lower temperature, we can calculate the change in height per degree Celsius and then apply that change to the given temperature range.
1. Calculate the change in height per degree Celsius:
Change in height = 19.7 cm
Temperature range = 40 °C - (-9 °C) = 49 °C
Change in height per degree Celsius = Change in height / Temperature range
= 19.7 cm / 49 °C
≈ 0.402 cm/°C
2. Apply the change to the lower temperature:
Change in height at the lower temperature = Change in height per degree Celsius * Change in temperature
= 0.402 cm/°C * (-9 °C)
≈ -3.618 cm
3. Subtract the change in height from the original height:
Height at lower temperature ≈ Original height - Change in height at lower temperature
= Original height - (-3.618 cm)
= Original height + 3.618 cm
Therefore, the approximate height at the lower temperature is the Original height + 3.618 cm. Unfortunately, the original height of the Eiffel Tower is not given in the question, so we cannot calculate the exact value.
a = 13*10^-6/oC = Temp. coeff.
h*a*(T2-T1) = 0.197.
h*13*10^-6(40-(-9)) = 0.197,
h*0.000637 = 0.197,
h = 309.3 m.