Dr. Terror has developed a new alloy called Ultranomium. He\\\'s testing a bar t

Question

Dr. Terror has developed a new alloy called Ultranomium. He's testing a bar that is 1.25 m long and has a mass of 362 grams. Using a carbon-dioxide infrared laser, he carfully heats the bar from 20.6 °C to 288 °C. Part A: If the bar absorbs 8.93 × 104 J of energy during the temperature change, what is the specific heat capacity (c) of the Ultranomum? Part B: He notices that at this new temperature, the bar's length has increased by 1.62 × 10-3 m. What is the coefficient of linear expansion () for the new alloy?

Explanation / Answer

Given Data

mass of bar, m = 362 g
length of bar, L = 1.25 m
change in temp, T = 288 – 20.6 = 267.4 C = 267.4 + 273.15 = 540.55
heat absorbed, Q = 8.93 × 104 J = 89300 J

m*C*T = Heat absorbed

solving for heat capacity, C :
C = Heat absorbed/m*T
C = 89300 / (362 *(540.55) )
C = 0.456 J/g*K

Part 2 :
Extension, L` = 0.00162 m
Net length = 1.25 + 0.00162 = 1.25162 m

In linear expansion we have :
(Expansion / original Length) = alpha * del(t)

Solving for coefficient of linear expansion, alpha :

alpha = ( L`/L ) / del(t)
alpha = (0.00162/1.25) / (288 – 20.6)
alpha = 4.85 * 10^-6 C^-1

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