1..........At what temperature of 0^C steel rod & copper rod have length of 80.1cm and 99.9cm respectively. At what temperature will the 2 rods have the same length.

Question

1..........At what temperature of 0^C steel rod & copper rod have length of 80.1cm and 99.9cm respectively. At what temperature will the 2 rods have the same length.

Coefficients of linear expansion (per °C) copper rod----.000017 steel rod-------.000012

2.....The length of a brass bar increase from 4.001m into 4.0030 m. find the final temperature of the bar if the initial temperature was 0 Celsius.
Coefficients of linear expansion (per °C) brass----- .000019

Answer 1

I will be happy to critique your work. These are straightforward uses of simple equations.

Answer 2

Your question #1 still contains a typo error

Answer 3

To calculate the temperature at which two rods have the same length, we can use the formula for linear expansion:

ΔL = α * L * ΔT

where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the initial length
ΔT is the change in temperature

Let's start with the first question:

1. Find the temperature at which the steel rod and copper rod have the same length:

Given:
Initial length of steel rod (L1) = 80.1 cm
Initial length of copper rod (L2) = 99.9 cm
Coefficient of linear expansion for steel (α1) = 0.000012 per °C
Coefficient of linear expansion for copper (α2) = 0.000017 per °C

Let's assume the change in length for both rods is the same, ΔL1 = ΔL2 = ΔL.
Also, let the temperature change be ΔT.

For the steel rod:
ΔL1 = α1 * L1 * ΔT
ΔL1 = 0.000012 * 80.1 * ΔT

For the copper rod:
ΔL2 = α2 * L2 * ΔT
ΔL2 = 0.000017 * 99.9 * ΔT

Since ΔL1 = ΔL2:
0.000012 * 80.1 * ΔT = 0.000017 * 99.9 * ΔT

Simplifying the equation:
0.000009612ΔT = 0.0016983ΔT
0.001688688ΔT = 0

This equation shows that the change in temperature doesn't affect the lengths of the two rods. Therefore, the temperature at which the two rods have the same length is irrelevant in this situation.

Moving on to the second question:

2. Find the final temperature of the brass bar:

Given:
Initial length of the brass bar (L) = 4.001 m
Final length of the brass bar (L') = 4.003 m
Coefficient of linear expansion for brass (α) = 0.000019 per °C

Let's assume the change in length is ΔL = L' - L = 4.003 - 4.001 = 0.002 m.

ΔL = α * L * ΔT
0.002 = 0.000019 * 4.001 * ΔT

Simplifying the equation:
0.000076019ΔT = 0.002
ΔT ≈ 26.306 °C

Therefore, the final temperature of the brass bar is approximately 26.306 °C when the initial temperature is 0 °C.