Question

A 25. 0 g block of copper (specific heat capacity 0. 380 J/g･°C) at 88. 0 °C is placed into 500. 0 g of water initially at 20. 0 °C. What is the change in temperature (in °C) of the copper block? (The specific heat capacity of water is 4. 184 J/g･°C)

Answer 1

-67.3 °C

Explanation:

You want the change in temperature of a 25 g copper block placed in 500 g of water. The initial temperature of the copper is 88 °C, and that of the water is 20 °C. The respective specific heat capacities are 0.380 and 4.184 J/(g·°C).

Setup

Let x represent the change in temperature of the copper block in °C. Then the final temperature of the copper and water is (88+x). The energy input required to change the temperature of the copper is ...

0.380 J/(g·°C) × 25.0 g × x

The energy input required to change the temperature of the water from 20 °C to (88+x) °C is ...

4.184 J/(g·°C) × 500 g × ((88+x) -20)

There is no external energy input to the system, so the net energy change is zero:

[0.380 J/(g·°C) × 25.0 g × x] + [4.184 J/(g·°C) × 500 g × ((88+x) -20)] = 0

Solution

Simplifying the equation, recognizing that the units of x are °C, we have ...

142256 +2101.5x = 0

x = -142256/2101.5 ≈ -67.6926

The change in temperature of the copper block is about -67.7 °C.