17. An aluminum rod of length 1.8cm at 100C is heated to produce a difference in length of 0.007m. Calculate the temperature to which it is heated (Liner expansivity of aluminum= 2.3 x 10-5 K-1)

To solve this problem, we need to use the formula for linear expansion, which is:

ΔL = α * L * ΔT

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

We are given: ΔL = 0.007 m = 0.7 cm (since 1m = 100cm), α = 2.3 x 10^-5 K^-1, L = 1.8 cm.

We are asked to find ΔT, which is the change in temperature.

Rearranging the formula to solve for ΔT, we get:

ΔT = ΔL / (α * L)

Substituting the given values into the formula, we get:

ΔT = 0.7 cm / ((2.3 x 10^-5 K^-1) * 1.8 cm)

Solving this gives us:

ΔT ≈ 16920.29 K

This is the change in temperature. However, we are asked to find the final temperature. The initial temperature was 100C, which is 373.15K (since 0C = 273.15K).

So, the final temperature T is:

T = initial temperature + ΔT T = 373.15K + 16920.29K T ≈ 17293.44 K

So, the aluminum rod is heated to a temperature of approximately 17293.44 K.

To solve this problem, we need to use the formula for linear expansion, which is:

ΔL = α * L * ΔT

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

We are given: ΔL = 0.007 m (or 0.7 cm, to match the units of the original length), α = 2.3 x 10^-5 K^-1, L = 1.8 cm.

We are asked to find ΔT, the change in temperature.

Rearranging the formula to solve for ΔT gives us:

ΔT = ΔL / (α * L)

Substituting the given values into this equation gives us:

ΔT = 0.7 cm / ((2.3 x 10^-5 K^-1) * 1.8 cm)

Solving this equation gives us:

ΔT ≈ 15217.39 K

However, this is the change in temperature, not the final temperature. The problem states that the initial temperature was 100°C, which is equivalent to 373.15 K.

Therefore, the final temperature T is:

T = 373.15 K + 15217.39 K = 15590.54 K

So, the aluminum rod was heated to a temperature of approximately 15590.54 K.