Calculate how much a 1.1 m slab of lead will expand if heated from -68 °C to 26 °C. Express your answer in m, cm, & in.
1 in = 2.54 cm.
To calculate the expansion of the lead slab, we need to use the linear expansion coefficient of lead. The linear expansion coefficient (α) represents how much a material expands per unit length when heated.
First, let's calculate the change in temperature:
Change in temperature = final temperature - initial temperature
ΔT = 26 °C - (-68 °C)
ΔT = 26 °C + 68 °C
ΔT = 94 °C
Next, we need to determine the linear expansion coefficient of lead. The linear expansion coefficient for lead is given as α = 0.000029 (1/°C).
Now, we can calculate the expansion in meters:
Expansion in meters = linear expansion coefficient * initial length * ΔT
Expansion in meters = 0.000029 (1/°C) * 1.1 m * 94 °C
Expansion in meters ≈ 0.0032384 m
To convert the expansion from meters to centimeters:
Expansion in centimeters = Expansion in meters * 100 cm/m
Expansion in centimeters ≈ 0.0032384 m * 100 cm/m
Expansion in centimeters ≈ 0.32384 cm
To convert the expansion from centimeters to inches:
Expansion in inches = Expansion in centimeters / 2.54 cm/in
Expansion in inches ≈ 0.32384 cm / 2.54 cm/in
Expansion in inches ≈ 0.12755 in
Therefore, the expansion of a 1.1 m slab of lead when heated from -68 °C to 26 °C is approximately 0.0032384 m, 0.32384 cm, and 0.12755 in.