🤓 Based on our data, we think this question is relevant for Professor Michael's class at UTEP.

Problem

A student constructs a "coffee cup" calorimeter that contains 83.6 grams of water, at 19.7°C, in a double cup set up with a thermometer and a cork cover. A piece of copper with a mass of 101.7 grams was heated to a certain temperature and placed in the calorimeter. Then the calorimeter was allowed to equilibrate and the thermometer recorded a temperature of 28.3 °C after the equilibration. Determine the temperature to which the copper piece was heated initially. (The specific heat of copper is 0.385 J/g °C and the specific heat of water is 4.184 J/g °C)

a. 105.1 °C

b. 85.4 °C

c. 142.0 °C

d. 29.0 °C

e. 48.5 °C

Solution

We’re being asked to determine the temperature at which the copper piece was heated *initially*.

We will use the heat released by the copper piece to calculate its initial temperature. Recall that heat can be calculated using the following equation:

$\overline{){\mathbf{q}}{\mathbf{=}}{\mathbf{mc}}{\mathbf{\u2206}}{\mathbf{T}}}$

q = heat, J

• **+q** → **absorbs **heat

• **–q** → **l****oses **heat

m = mass (g)

c = specific heat capacity = J/(g·°C)

ΔT = T_{f} – T_{i} = (°C)

**Based on the given system:**