Question

You have two rods, one is made of aluminum and the other is made of Pyrex glass. At T = 0℃, the length of the aluminum rod is LA???? = 3.070 m, and the length of the Pyrex rod is LPyrex = 3.100 m. You are given that the coefficient of linear expansion for aluminum is ????A???? = 24 × 10−6 1 ℃ and ????Pyrex = 3.3 × 10−6 1 ℃ . Please keep 4 significant figures in all your results. a. At what temperature will the aluminum rod and the Pyrex rod have the same length?

Answer 1

The temperature at which the aluminum and Pyrex rods have the same length, set up an equation using the formula for linear thermal expansion. The temperature at which they have the same length is approximately 423.6°C.

Step-by-step explanation:

To find the temperature at which the aluminum rod and the Pyrex rod have the same length, we can set up an equation using the formula for linear thermal expansion. The change in length of each rod is given by the product of their original lengths, the coefficient of linear expansion, and the change in temperature. Let's call the temperature at which they have the same length T. We can set up the following equation:

LAl + (αAl)LAl(ΔT) = LPyrex + (αPyrex)LPyrex(ΔT)

Substituting the given values, we get:

3.070 + (24 × 10-6) × 3.070(ΔT) = 3.100 + (3.3 × 10-6) × 3.100(ΔT)

Simplifying the equation, we find that the temperature at which the rods have the same length is approximately 423.6°C.

Answer 2

Step-by-step explanation:

The length of rod after rise in temperature can be calculated by the formula

`l_t` = l₀ ( 1 + αΔt)

`l_t` is increased length , l₀ is original length , α is coefficient of thermal expansion and Δt is rise in temperature.

Let after rise in temperature of Δt in both , they become equal in length

3.07 ( 1 + 24 x 10⁻⁶Δt ) = 3.1 ( 1 + 3.3 x 10⁻⁶ Δt )

3.07 + 73.68 x 10⁻⁶Δt = 3.1 + 10.23 x 10⁻⁶ Δt

.03 = 63.45 x 10⁻⁶Δt

Δt = 472.8

At 472.8 °C they will have same length .