Question 5.3.2: a. Determine the amount of heat energy that is associated wi......
a. Determine the amount of heat energy that is associated with heating a 154-g iron bar from 20.0 ºC to 485 ºC.
b. Calculate the final temperature reached when 324 J of heat is added to a 24.5-g iron bar initially at 20.0 ºC.
a. You are asked to calculate the amount of heat (q) transferred to an iron bar.
You are given the mass of the iron bar and the initial and final temperature of the iron.
Use Equation 5.5 to calculate the amount of heat transferred to the iron bar.
c, specific heat capacity (J/g·°C) = \frac{q,\text{ heat energy absorbed (J)}}{m, \text{mass (g) }\times \Delta T, \text{change in temperature (°C) }} (5.5)
c_{Fe} = 0.449 J/g · ºC
m = 154 g
∆T = T_{final} − T_{initial} = 485 ºC − 20.0 ºC = 465 ºC
q = m × c_{Fe} × ∆T = (154 g)(0.449 J/g · ºC)(465 ºC) = 3.22 × 10^{4} J
Is your answer reasonable? The temperature change was relatively large, so you would expect a large amount of heat energy was transferred to the iron.
b. You are asked to calculate the final temperature when a given amount of heat is added to an iron bar.
You are given the amount of energy, the mass of the bar, and the initial temperature of the bar.
Use Equation 5.5 to calculate the change in temperature of the iron bar.
c_{Fe} = 0.449 J/g · ºC
m = 24.5 g
q = 324 J
\Delta T=\frac{q}{m\times c_{Fe}}=\frac{324\text{ J}}{(24.5 \text{ g})(0.449\text{ J/g}\cdot ^{\circ }\text{C})} = 29.5 °C
The temperature of the iron bar therefore increases from 20.0 ºC to 49.5 ºC.
Is your answer reasonable? A relatively small amount of heat energy was transferred to the iron bar (less than in part a. of this example problem), so you would expect a relatively small temperature change.