Question

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?

Answer 1

`d_(steel) = 25.026 cm`

Step-by-step explanation:

Given data:

diameter of cylinder 25 cm

`T_1 = 20` degree celcius

`T_2 = 150` degree celcius

from the information given in the question we have

`\delta_(brass)  + 25 + \delta_(steel) + d_(steel)`

`25* \alpha * \delta T +  25 =  d_(steel) * \alpha* \delta T + d_[steel}`

`25(1+ \alpha_(brass) * \delta T) = d_s(1+ \alpha * \delta T)`

SOLVING FOR[/tex] d_{steel}[/tex]

`d_(steel) = (25(1+\alpha_(brass) * \delta t)/(1+ \alpha_(steel)* \delta T)`

`d_(steel) = (25(1+ 3* 10^(-5) (C^0)^(-1) * (150-20))/(1+ 1.2* 10^(-5) (C^0)^(-1) * (150-20))`

`d_(steel) = 25.026 cm`