9.2 - Energy Changes from Temperature
Energy change from a temperature change
- When a reaction happens in a solution, the energy given out or taken in shows up as a temperature change in the solution.
- That temperature change can be used to calculate the energy transferred.
Formula for energy transferred
Where:
- = Energy transferred, in joules (J)
- = Mass of the water or solution being heated or cooled, in grams (g); the mass of a solid added to it is not included
- = Specific heat capacity of the solution, in joules per gram per degree Celsius (J/g/°C); for water, about 4.2 J/g/°C
- = Temperature change, in degrees Celsius (°C)
Reading the direction
- Temperature rose → the reaction released energy into the solution → exothermic.
- Temperature fell → the reaction took energy out of the solution → endothermic.
Worked example - Energy from a temperature change
15.0 g of ammonium nitrate, NH4NO3, is dissolved in 85.0 g of water. The temperature of the solution falls from 23.7 °C to 12.3 °C. The specific heat capacity of the solution is 4.2 J/g/°C. Calculate the energy transferred.
Step 1 - Find the temperature change
ΔT = 12.3 − 23.7 = −11.4 °C, so the temperature change is 11.4 °C
The temperature fell, so the reaction took the energy in.
Step 2 - Find the mass of the solution in grams
The mass heated is the mass of the water; the mass of the dissolved solid is not added to it:
m = 85.0 g
Step 3 - Multiply m × c × ΔT
Q = 85.0 × 4.2 × 11.4 = 4,069.8 J
Step 4 - Round the answer
The masses and temperatures are all given to three significant figures, so:
Energy transferred = 4,070 J, which is 4.07 kJ
The temperature fell, so the energy was taken in from the solution and the reaction is endothermic.
Energy released per gram of a fuel
- Different fuels don't release the same amount of energy when they burn.
- To compare them fairly, compare the energy each releases for the same mass of fuel: the energy released per gram.
Stage 1 - Energy transferred to the liquid
Where:
- = Energy transferred to the liquid, in joules (J)
- = Mass of liquid heated, in grams (g); for water, 1 cm3 has a mass of 1 g
- = Specific heat capacity of the liquid, in joules per gram per degree Celsius (J/g/°C); for water, about 4.2 J/g/°C, but always use the value supplied with the question or on the data sheet, which may be given as 4.18
- = Temperature rise of the liquid, in degrees Celsius (°C)
Stage 2 - Energy per gram of fuel
Worked example - Energy per gram of a fuel
Ethanol is burned to heat 175 g of water. The temperature of the water rises from 19.5 °C to 45.5 °C, and 1.15 g of ethanol burns. The specific heat capacity of water is 4.2 J/g/°C. Calculate the energy released per gram of ethanol.
Step 1 - Find the temperature rise
ΔT = 45.5 − 19.5 = 26.0 °C
Step 2 - Find the mass of the liquid in grams
m = 175 g
Step 3 - Multiply m × c × ΔT
Q = 175 × 4.2 × 26.0 = 19,110 J
Step 4 - Divide the energy by the mass of fuel burned
19,110 ÷ 1.15 = 16,617.39 J per gram
Step 5 - Round the answer
The mass of water, the mass of ethanol and the two temperatures are all given to three significant figures, so:
Energy released per gram of ethanol = 16,600 J/g, which is 16.6 kJ/g