Final answer:
The period of a pendulum changes with temperature as the length of the pendulum changes due to thermal expansion. For a brass pendulum, we use the coefficient of linear expansion to calculate the change in length and then the change in period as the temperature increases from 19°C to 32°C.
Step-by-step explanation:
To calculate how much the period of the pendulum changes with temperature, we will use the formula for the period of a simple pendulum and the coefficient of linear expansion (alpha) for brass. The formula for the period of a simple pendulum is given by T = 2π√(L/g), where L is the length of the pendulum, and g is the acceleration due to gravity. The length of the pendulum changes with temperature according to the equation L = L0(1 + αΔT).
Given that α for brass is 18 × 10-6°C−1 and the initial calibrated temperature is 19°C with a period of 1 second, we want to find the change in period when the temperature increases to 32°C. The change in temperature, ΔT, is 32°C - 19°C = 13°C. Therefore, the new length of the pendulum, Lnew, will be L0(1 + αΔT) = L0(1 + 18 × 10-6× 13).
The change in the period, ΔT, can be found using the ratio of the new period, Tnew, to the original period, T0, which is proportional to the square root of the lengths. Thus, Tnew/T0 = √(Lnew/L0). We find ΔT by subtracting the original period from the recalculated period.
After doing the math, we find a small change in the period of the pendulum clock. While an exact answer is not provided here, this is the correct approach to solving the problem.