Heat Capacity Example Problem - Find Final Temperature

This worked 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.