As a new mechanical engineer for Engines Inc., 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°C and 150.0°C. Assume that the coefficients of expansion are constant over this temperature range. If the piston just fits inside the chamber at 20.0°C, will the engines be able to run at higher temperatures? Explain.

Verified step by step guidance

1. Identify the materials involved: brass for the pistons and steel for the cylinders. Each material has a different coefficient of linear expansion, which will affect how much they expand when heated.
2. Understand the concept of thermal expansion: When materials are heated, they expand. The amount they expand can be calculated using the formula for linear expansion: $\mathrm{\Delta L}=\alpha L\mathrm{\Delta T}$, where $\mathrm{\Delta L}$ is the change in length, $\alpha$ is the coefficient of linear expansion, $L$ is the original length, and $\mathrm{\Delta T}$ is the change in temperature.
3. Calculate the expansion of both the brass piston and the steel cylinder from 20.0°C to 150.0°C using their respective coefficients of linear expansion. This will help determine if the piston will still fit inside the cylinder at the higher temperature.
4. Compare the expansions: If the brass piston expands more than the steel cylinder, it may not fit inside the cylinder at the higher temperature. Conversely, if the steel cylinder expands more, the piston will still fit.
5. Conclude based on the comparison: If the piston expands more than the cylinder, the engine may not run properly at higher temperatures due to the piston not fitting. If the cylinder expands more, the engine should run without issues at higher temperatures.

Key Concepts

Thermal Expansion

Thermal expansion refers to the tendency of matter to change in volume in response to a change in temperature. When materials are heated, their particles move more vigorously, causing the material to expand. This concept is crucial for understanding how the brass pistons and steel cylinders will behave as the temperature increases from 20.0°C to 150.0°C.

Coefficient of Linear Expansion

The coefficient of linear expansion quantifies how much a material expands per degree change in temperature. It is specific to each material and is assumed constant over the given temperature range. Knowing the coefficients for brass and steel allows us to predict how much each will expand, which is essential for determining if the piston will continue to fit inside the cylinder at higher temperatures.

Material Compatibility

Material compatibility involves understanding how different materials interact under varying conditions, such as temperature changes. In this context, it is important to assess whether the expansion rates of brass and steel are compatible, ensuring that the piston can slide smoothly within the cylinder without causing mechanical issues or failure at elevated temperatures.