A grandfather clock is controlled by a swinging brass pendulum that is 1.2 m long at a temperature of 27°C. (a) What is the length of the pendulum rod when the temperature drops to 0.0°C? (Round your answer to four significant figures.) mm

L2 = 1.1994 m

the length of the pendulum rod when the temperature drops to 0.0°C is 1.1994 m

Explanation:

Given;

Initial length L1 = 1.2m

Initial temperature T1 = 27°C

Final temperature T2 = 0.0°C

Linear expansion coefficient of brass x = 1.9 * 10^-5 / °C

The change i length ∆L;

∆L = L2 - L1

L2 = L1 + ∆L ... 1

∆L = xL1 (∆T)

∆L = xL1 (T2 - T1) ... 2

Substituting the given values into equation 2;

∆L = 1.9 * 10^-5 / °C * 1.2m * (0 - 27)

∆L = 1.9 * 10^-5 / °C * 1.2m * ( - 27)

∆L = - 6.156 * 10^-4 m

From equation 1;

L2 = L1 + ∆L

Substituting the values;

L2 = 1.2 m + ( - 6.156 * 10^-4 m)

L2 = 1.2 m - 6.156 * 10^-4 m

L2 = 1.1993844 m

L2 = 1.1994 m

the length of the pendulum rod when the temperature drops to 0.0°C is 1.1994 m