Answer:
A. 92.88 °C
B. 401.535 °C
Explanation:
So, the overheating system is going to be based on the principle of thermal linear expansion. The behavior of this principle is ruled by the equation:
∆L= L_i * ∆T * α
Where α is a coefficient of linear expansion. For a cylinder made from polycarbonate α = 70,2*10^(-6) °C^(-1) and for a cylinder made from cast iron α = 12*10^(-6) °C^(-1). If we isolate the term of the temperature’s difference, we have:
∆L/(L_i * α) = ∆T → T_f = T_i + ∆L/(L_i * α)
Replacing the values, for the case of the Polycarbonate we have:
T_f = T_i + ∆L/(L_i * α) = 23°C+0,0273cm/(6,01cm *70,2 * 10^(-6)°C^(-1) ) = 92,88 °C
Replacing the values, for the case of the Cast Iron we have:
T_f = T_i +∆L/(L_i * α) = 23°C + 0,0273cm/(6,01cm * 12 * 10^(-6) °C^(-1) ) = 401,535 °C
As we see, is way better to use the polycarbonate in this application.
Have a nice day. Let me know if I can help you with anything else. :D
