Question

The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is 35.0°C. What will its height be on a day when the temperature falls to −10.0°C? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.

a) 169.92 m
b) 169.88 m
c) 169.80 m
d) 169.75 m

Answer 1

The height of the Washington Monument on a day with a temperature of -10.0°C would be approximately 169.92 m. The correct answer is option A.

Step-by-step explanation:

The height of the Washington Monument on a day when the temperature is 35.0°C is 170.00 m. To calculate the height of the monument on a day when the temperature falls to -10.0°C, we need to consider the thermal expansion of limestone. Assuming that the thermal coefficient of expansion for limestone is the same as that of marble, we can use the equation:

ΔL = L * α * ΔT

where ΔL is the change in length, L is the original length, α is the thermal coefficient of expansion, and ΔT is the temperature change. For limestone, the thermal coefficient of expansion is approximately 9 x 10^-6 °C^-1. Plugging in the values, we get:

ΔL = 170.00 m * (9 x 10^-6 °C^-1) * (-10.0°C - 35.0°C)

ΔL = 170.00 m * (9 x 10^-6 °C^-1) * (-45.0°C)

ΔL ≈ -0.0765 m

Therefore, the height of the Washington Monument on a day when the temperature falls to -10.0°C is approximately 169.92 m.