Question

Many automobile engines have cast-iron cylinders and aluminium pistons. What kinds of problems could occur if the engine gets too hot? (The coefficient of volume expansion of cast iron is approximately the same as that of steel.)

Short answer

The friction between the piston and the cast iron will prevent the piston move freely inside the Iron cast and would cause damage to the engine.

Step-by-step solution

Thermal Expansion

The formula of volume expansion due to thermal energy is$\mathbf{\delta V}\mathbf{=}\mathbf{V}\mathbf{\times }\mathbf{\beta }\mathbf{\times }\mathbf{\delta T}$.

Coefficients of expansion

For the same volume $\left(V\right)$ and change in temperature $\mathbf{\left(}\mathbf{\delta V}\mathbf{\right)}$, the change in volume $\mathbf{\left(}\mathbf{\delta T}\mathbf{\right)}$will depend upon the coefficient of expansion. Now, role="math" localid="1663819662423" $\mathbf{3}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{\hspace{0.33em}}{\mathbf{K}}^{\mathbf{-}\mathbf{1}}$and ${\mathbf{\beta }}_{\mathbf{AI}}\mathbf{=}\mathbf{7}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}{\mathbf{K}}^{\mathbf{-}\mathbf{1}}$.

Clearly aluminium has larger thermal expansion coefficient than steel and causes high heat capacity absorbed by the piston.

Problem faced by the automobile

The problem that the automobile will face is preventing the piston move freely inside the Iron cast and would cause damage for the engine due to friction between the piston and the cast iron.