In an experiment, 74.3 g of metallic copper was heated to 100.0°C and then quickly dropped into 200.0 mL of water in a calorimeter. The heat capacity of the calorimeter with the water was
875 J/°C. The initial temperature of the calorimeter was 27.5°C, and the final temperature after addition of the metal was 29.8°C. What is the value of the specific heat capacity of copper?

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of heat released by the copper and then equate it to the heat absorbed by the water and the calorimeter.

Heat released by the copper:

q = mcΔT

where q is the heat released, m is the mass of copper, c is its specific heat capacity, and ΔT is the change in temperature.

We know the mass of copper (74.3 g) and the initial and final temperatures (100.0°C and 29.8°C, respectively). We don't know c, so we'll call it x:

q = (74.3 g)(x)(100.0°C - 29.8°C)

q = 463540x J

Heat absorbed by the water and calorimeter:

q = CΔT

where q is the heat absorbed, C is the total heat capacity of the water and calorimeter (875 J/°C), and ΔT is the change in temperature (29.8°C - 27.5°C = 2.3°C).

q = (875 J/°C)(2.3°C)

q = 2012.5 J

Now we set the two expressions for q equal to each other and solve for x:

463540x J = 2012.5 J

x = 0.00434 J/(g°C)

Since we need the answer in units of J/(g°F), we need to convert the units:

0.00434 J/(g°C) x (1 cal/4.184 J) x (1°F/1.8°C) = 0.386 J/(g°F)

Therefore, the specific heat capacity of copper is 0.386 J/(g°F) or choice C.

In an Experiment, 74