Thermal Expansion of Brass piston in Steel cylinder

In summary, the task at hand is to design brass pistons to slide inside steel cylinders for use in engines operating between 20.0 and 150.0 degrees Celsius. With the given coefficients of expansion, the minimum diameter of the cylinders at 20.0 degrees Celsius must be larger than the diameter of the brass pistons to account for expansion at higher temperatures. The exact calculations for determining the minimum diameter require further information about the height of the cylinder, but the concept is to allow for the brass piston to expand freely at higher temperatures without creating a gap between the piston and the cylinder.
  • #1
NickP89
18
0

Homework Statement


You have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0 degrees Celsius and 150.0 degrees Celsius. Assume that the coefficients of expansion are constant over this temperature range.
If the cylindrical pistons are 25.000 cm in diameter at 20.0 degrees C, what should be the minimum diameter of the cylinders at that temperature so the pistons will operate at 150.0 degree C?

Homework Equations


ΔV=βV(Initial)ΔT for Volume Expansion, where β is the coefficient of volume expansion
ΔA=2αA(initial)ΔT for Area Expansion, where α is the coefficient of linear expansion

The coefficient of volume expansion for brass is 6*10^-5 and for steel is 3.6*10^-5. The coefficient of linear expansion for brass is 2*10^-5 and for steel is 1.2*10^-5.

Volume of cylinder: pi*r^2*h

The Attempt at a Solution


I am not sure if I have to use the volume expansion equation or the area expansion equation. I understand that the cylinders are solids and would undergo volume expansion but I wasn't given a height of the cylinder. I tried assigning a value of 1cm for the height but I don't think that's O.K. I tried using the area expansion but also got numbers that were not realistic.

Attempt at solution:

ΔV=(6*10^-5)(130K)(pi*(12.5cm)^2*h)=(3.83cm)h for the brass piston

The steel cylinder would also expand:

ΔV=(3.6*10^-5)(130K)(pi*r^2*h)=0.0147*r^2*h

I really don't know where to go from here, I know that the brass will expand more than the steel, and that the steel cylinder certainly has to be bigger than the brass piston at 20 degrees celsius, but I don't know how to relate the two. Any direction and help will be appreciated very much.
 
Physics news on Phys.org
  • #2
Isn't the case that the when the brass piston reaches 150 degree celsius, then the inner diameter of the steel cylinder(also at 150 deg) must be the same as the outer diameter of the piston? There will be no gap between the piston and the cylinder at 150 deg, but there will be at 20 deg. You must design the cylinder so that the brass piston is allowed to expand freely?
 
Last edited:

1. What is thermal expansion?

Thermal expansion is the tendency of a material to expand or contract in response to changes in temperature.

2. How does thermal expansion affect brass pistons in steel cylinders?

As the temperature of the brass piston and steel cylinder increases, the materials will expand at different rates. This can cause the piston to become stuck in the cylinder or create gaps between the two components.

3. What factors can affect the thermal expansion of brass and steel?

The thermal properties and composition of the materials, as well as the temperature difference and duration of exposure, can all affect the degree of thermal expansion in brass and steel.

4. How can thermal expansion be accounted for in the design of a brass piston in a steel cylinder?

Engineers and designers can account for thermal expansion by using materials with similar coefficients of thermal expansion, incorporating gaps or allowances for expansion, or using materials that can withstand high temperatures without significant expansion.

5. What are some practical applications of understanding thermal expansion in brass and steel?

Understanding thermal expansion is crucial in designing and constructing various objects and structures, such as bridges, pipelines, and engines. It also plays a significant role in the production of precision instruments and machinery, where small changes in size due to thermal expansion can greatly affect performance.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
633
  • Mechanical Engineering
Replies
1
Views
104
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
868
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
922
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
3K
Back
Top