This example problem demonstrates how to calculate the final temperature of a substance when given the amount of energy used, the mass and initial temperature.

## Problem

300 grams of ethanol at 10 °C is heated with 14640 Joules of energy. What is the final temperature of the ethanol?

**Useful Information**: The specific heat of ethanol is 2.44 J/g·°C.

## Solution

Use the formula

q = mcΔT

Where

- q = Heat Energy
- m = Mass
- c = Specific Heat
- ΔT = Change in temperature.

14640 J = (300 g)(2.44 J/g·°C)ΔT

Solve for ΔT:

- ΔT = 14640 J/(300 g)(2.44 J/g·°C)
- ΔT = 20 °C
- ΔT = T
_{final}- T_{initial} - T
_{final}= T_{inital}+ ΔT - T
_{final}= 10 °C + 20 °C - T
_{final}= 30 °C

**Answer**:** **The final temperature of the ethanol is 30 °C.

## Final Temperature After Mixing

When you mix together two substances with different initial temperatures, the same principles apply. If the materials don't chemically react, all you need to do to find the final temperature is to assume that both substances will eventually reach the same temperature.

### Problem

Find the final temperature when 10.0 grams of aluminum at 130.0 °C mixes with 200.0 grams of water at 25 °C. Assume no water is lost as water vapor.

### Solution

Again, you use q = mcΔT, except you assume q_{aluminum} = q_{water} and solve for T, which is the final temperature. You need to look up the specific heat values (c) for aluminum and water. This solution uses 0.901 for aluminum and 4.18 for water:

- (10)(130 - T)(0.901) = (200.0)(T - 25)(4.18)
- T = 26.12 °C