Thermal expansion in heat engine

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To ensure a brass piston with a diameter of 25 cm at 20 degrees Celsius operates without rubbing in a steel cylindrical chamber at 150 degrees Celsius, the minimum initial diameter of the cylinder must account for thermal expansion. The coefficients of linear expansion for brass and steel are 2x10^-5 and 1.2x10^-5, respectively. Using the formula for linear expansion, the change in diameter for both materials can be calculated based on the temperature increase of 130 degrees Celsius. Since diameter is a linear dimension, the focus should be on linear thermal expansion rather than volume. Proper calculations will yield the necessary initial diameter of the steel cylinder to accommodate the expanded brass piston.
skittlebrew
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A brass piston of diameter 25 cm at 20 degrees C must be able to function at 150 degrees C.
In order to do so it must fit inside a steel cylidrical chamber. What must the minimum initial diameter of the cylinder be so that the piston never rubs against it.
alpha=2x10^-5 for brass
alpha=1.2x10^-5 for steel
dT=130 degrees C

dL=alpha*L0*dT
dV=beta*V0*dT

I don't know whether this is Volume or linear thermal expansion. I think it is volume but there is no given value for length of the piston or cylinder so initial volume and delta V are unknown.
 
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Hint: diameter is a linear dimension quantity.

p.s. welcome to PF.
 
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