The height of the Washington Monument is measured to be 170 m on a day when its temperature is 35.0°C. What will the change in its height be on a day when its temperature falls to -12.0°C? Although the monument is made of limestone, take the thermal coefficient of expansion to be that of marble.
(answer to be in cm)
To = 9C/5 + 32 = 9*35/5 + 32 = 95oF.
T = 9*(-12)/5 + 32 = 10.4oF.
a max = 7.9*10^-6/oF.
Change = a*(T-To)ho
7.9*10^-6*(10.4-95)*170 = -11.36 cm.
Change = 11.36 cm decrease
Change = coefficient*Length*Difference in Temp
(2.5*10^-6)*170*(-12-35) = -.019975 meters
-.0199m = -1.99cm
To determine the change in height of the Washington Monument, we need to use the formula for linear thermal expansion:
ΔL = α * L * ΔT
where:
ΔL represents the change in length,
α represents the thermal coefficient of expansion,
L represents the original length, and
ΔT represents the change in temperature.
First, we need to find the thermal coefficient of expansion for marble. Let's assume it is 1.2 x 10^-5 per °C.
Given:
Original height (L) = 170 m
Initial temperature (T1) = 35.0°C
Final temperature (T2) = -12.0°C
Now, let's calculate the change in height:
ΔT = T2 - T1
= -12.0°C - 35.0°C
= -47.0°C
ΔL = α * L * ΔT
= 1.2 x 10^-5 °C^-1 * 170 m * (-47.0°C)
= -0.1192 m
To convert the change in height from meters to centimeters, we can multiply by 100:
-0.1192 m * 100 cm/m = -11.92 cm
Therefore, the change in height of the Washington Monument on a day when its temperature falls to -12.0°C is approximately -11.92 cm.
To find the change in height of the Washington Monument when the temperature changes, we can use the formula for thermal expansion:
Change in height = original height * coefficient of linear expansion * change in temperature
First, let's convert the original height of the Washington Monument from meters to centimeters:
Original height = 170 m = 170 * 100 cm = 17,000 cm
Next, we need to find the coefficient of linear expansion for marble, which is the material assumed for the Washington Monument. The coefficient of linear expansion for marble is approximately 0.000014 /°C.
Now, we can plug in the values into the formula:
Change in height = 17,000 cm * 0.000014 /°C * (final temperature - initial temperature)
Final temperature = -12.0°C
Initial temperature = 35.0°C
Change in height = 17,000 cm * 0.000014 /°C * (-12.0°C - 35.0°C)
Simplifying the equation:
Change in height = 17,000 cm * 0.000014 /°C * (-47.0°C)
Change in height = -10.062 cm
Therefore, the change in height of the Washington Monument when the temperature falls to -12.0°C would be approximately -10.062 cm.