Final answer:
An iron pendulum clock will lose approximately 5.184 seconds per day when the temperature increases from 20°C to 30°C, given the linear expansivity of iron is 12×10⁻⁶ per kelvin. This is calculated using the relationship between temperature change, linear expansivity, and the period of a pendulum.
Step-by-step explanation:
The student is asking about the time a pendulum clock will lose or gain when the temperature is increased from 20°C to 30°C given that the linear expansivity (α) of iron is 12×10⁻⁶ per kelvin. Since the pendulum clock keeps correct time at 20°C, any change in temperature will affect the length of the pendulum rod and thus, its period.
We use the formula for the change in the length of the pendulum rod ΔL = α × L × ΔT, where L is the original length and ΔT is the change in temperature. The period of the pendulum T is given by T = 2π√(L/g), therefore as L increases, T increases as well, causing the clock to run slower.
For a small temperature change ΔT, we can use the approximation that the change in the period ΔT is proportional to αΔT/2. If we consider one day to be 86400 seconds, we can calculate the time lost per day (Δt) by the clock using Δt = T×αΔT/2. Substituting the given values, we get Δt = 86400 s × 12×10⁻⁶/K × 10 K / 2. This yields Δt = 5.184 seconds lost per day at a temperature of 30°C.