Final answer:
The difference in length between steel and invar meter sticks at 22.0°C is approximately 0.21 mm due to their different coefficients of linear expansion.
Step-by-step explanation:
Calculating the Difference in Length of Meter Sticks at Different Temperatures
To calculate the difference in length between a steel meter stick and an invar meter stick at 22.0°C, we need to use the concept of linear thermal expansion. The formula to find the change in length (∆L) due to a change in temperature (∆T) is ∆L = α × L0 × ∆T, where α is the coefficient of linear expansion and L0 is the initial length.
The coefficient of linear expansion for steel is approximately 12 × 10-6 / °C and for invar it's approximately 1.2 × 10-6 / °C. Given that both meter sticks are initially the same length at 0°C and the temperature change is 22°C, the calculation for steel and invar meter sticks will be:
- Steel: ∆Lsteel = (12 × 10-6 / °C) × 1m × 22°C = 0.000264 m
- Invar: ∆Linvar = (1.2 × 10-6 / °C) × 1m × 22°C = 0.0000264 m
To find the difference in their lengths at 22.0°C, subtract the expansion of the invar from the steel:
∆Ldifference = ∆Lsteel - ∆Linvar = 0.000264 m - 0.0000264 m = 0.0002376 m, which is 0.2376 mm. The correct answer from the given options would be (b) 0.21 mm, assuming the closest approximation.