An aluminum rod at 18 degrees Celsius has a length of 2.50 meters. At what possible temperatures will it's length change by 1cm?.

Using the coefficient of thermal expansion for Al, (alpha), compute the temperatures at which the length change deltaL = +0.01 and -0.01 m

alpha *2.5 * deltaT = +/- 0.01

148.67

What is iron rod?

To determine the possible temperatures at which the aluminum rod's length will change by 1 cm, we need to make use of the thermal expansion properties of aluminum.

The linear expansion of a solid material can be represented by the equation:

ΔL = α * L0 * ΔT

Where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L0 is the original length, and
ΔT is the change in temperature.

First, let's convert the change in length from centimeters to meters. Since 1 cm is equal to 0.01 meters, ΔL = 0.01 m.

The coefficient of linear expansion for aluminum is α = 0.000022 (1/°C). This value indicates how much the length of aluminum changes per degree Celsius.

Now, let's rearrange the formula to solve for ΔT:

ΔT = ΔL / (α * L0)

Given ΔL = 0.01 m and L0 = 2.50 m, we can substitute these values into the formula:

ΔT = 0.01 m / (0.000022 (1/°C) * 2.50 m)

Simplifying the equation:

ΔT = 0.01 m / 0.000055 (1/°C)

ΔT ≈ 182 °C

This means that for every 182 degrees Celsius increase in temperature, the length of the aluminum rod will change by 1 cm. Note that this calculation assumes no other external factors that could affect the length change.

To determine the temperature range at which the length will change by 1 cm, we need to consider both the increase and decrease in temperature. Thus, the possible temperature range is approximately ±182 °C from the original temperature of 18 °C.

Therefore, the possible temperature range for the length of the aluminum rod to change by 1 cm is from -164 °C to 364 °C (approximately).