# Thermodynamics basic

• xiaoyaozizai
In summary, the rail temperature rises by 30 degrees Celsius, but the middle joint between the two parts of the rail rises upwards by much more due to the temperature change. The thermal expansion coefficient of steel is 1.2×10-5 K-1, so the middle joint would rise by 0.108 light years due to the temperature change.f

#### xiaoyaozizai

Homework Statement
A 30 m long steel rail is firmly secured to the ground at both ends . The rail temperature rises by 30 ° C in hot sunshine. Assume that the rail consists of two equally long parts that are articulated in the middle. How much does the middle joint rise upwards due to temperature change ? The thermal expansion coefficient of the steel is 1,2 × 10-5 K-1 .
Relevant Equations
I used the

30× (1.2×10-5) ×30

= 0.108

That's not the right answer. Did I use the wrong formula
30×（1.2×10-5）×30

= 0.108

Help

Last edited by a moderator:
You have calculated the amount by which the total length increases. By how much it rises is the question.
That depends on the shape. If it were a single length of rail, that is moderately advanced to calculate, but if I inderstand the question, because of the articulation the shape is two straight lines ∧ which is much easier.

Where did you get that crazy formula from?

Where did you get that crazy formula from?

Homework Statement:: A 30 m long steel rail is firmly secured to the ground at both ends . The rail temperature rises by 30 ° C in hot sunshine. Assume that the rail consists of two equally long parts that are articulated in the middle. How much does the middle joint rise upwards due to temperature change ? The thermal expansion coefficient of the steel is 1,2 × 10-5 K-1 .
Relevant Equations:: I used the

30× (1.2×10-5) ×30

= 0.108

That's not the right answer. Did I use the wrong formula
0.108 light years? Yeah, that's pretty unreasonable.

In the formula ##\Delta L = L_0 \alpha \Delta T##, what does ##\Delta L## represent? Is it what's being asked for in the problem?

Physics isn't about plugging numbers into some equation. It's about analyzing a situation and applying relatively few concepts to get to the desired result. You need to work on the analysis part.

• jbriggs444 and Lnewqban
0.108 光年？是的，这很不合理。

ok thank you

Where did you get that crazy formula from?
30×（1.2×10-5）×30 appears to be an attempt to write ##30 \text{ meters} \times \frac{1.2 \times 10^{-5}}{\text{K}} \times 30 \text{ K}## to obtain, supposedly, ##0.108 \text{ meters}##

However, taking 900 (close to 1000) and multiplying it by 1.2/100000 (close to 1/100000) does not yield something close to 1/10. Mathematical literacy allows one to sometimes notice when calculators return the wrong answer.

There is an order of magnitude error even before we get to the point of solving the correct problem. That part should be another couple of orders of magnitude to deal with.

30×（1.2×10-5）×30 似乎是尝试写 ##30 \text{meter} \times \frac{1.2 \times 10^{-5}}{\text{K}} \times 30 \text{ K}## 得到，据说，##0.108 \text{ 米}##

ok i know thank you for explaining