Final answer:
The specific heat of copper, when 450.00 cal of energy raises the temperature of 70.32 g of copper from 20.05ºC to 89.61ºC, is calculated to be approximately 0.387 J/gºC.
Step-by-step explanation:
To calculate the specific heat of copper given that 450.00 cal of thermal energy are absorbed by 70.32 g of solid copper, causing its temperature to rise from 20.05ºC to 89.61ºC, you use the formula q = mcΔT, where q is the heat absorbed, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.
First, convert calories to joules, knowing that 1 cal = 4.184 J, which gives q = 450.00 cal × 4.184 J/cal = 1882.8 J. Then, ΔT is the final temperature minus the initial temperature, so ΔT = 89.61ºC - 20.05ºC = 69.56ºC.
The specific heat c can now be found by rearranging the formula to c = q/(mΔT), and plugging in the values:
c = 1882.8 J / (70.32 g × 69.56ºC)
= 0.387 J/gºC.
Therefore, the specific heat of copper is approximately 0.387 J/gºC.