大象传媒

Multiple changes

relates only to the energy required for a change in temperature. relates only to the energy required for a change in state. If a change in of a material will cause it to change temperature and change state, both equations can be used.

Example

What happens when 1 kilogram (kg) of water at 75 degrees Celsius (掳C) is heated with 2.5 megajoules (MJ) (2,500,000 J)?

1. Some of the energy is used to raise the temperature of the water to 100掳C, so the energy needed to raise 1 kg of water by 25掳C is:

\(\Delta QE = mc \Delta \theta\)

\(\Delta QE = 1 \times 4,200 \times 25\)

\(\Delta QE = 105,000~J\)

2. Some of the remaining 2,395,000 J is then used to turn the boiling water into steam, so the energy needed to change 1 kg of water at 100掳C into steam at the same temperature is:

\(\Delta QE = mL\)

\(\Delta QE = 1 \times 2,260,000~J\)

\(\Delta QE = 2,260,000~J\)

The final amount of energy 2,500,000 - 2,260,000 - 105,000 = 135,000 J, is used to raise the temperature of the steam, and as steam has a specific heat capacity of 1859 J/kg掳C, the final temperature of the steam would be:

\(E = mc \Delta \theta\)

\(135,000 = 1 \times 1,859 \times \Delta \theta\)

\(\Delta \theta = \frac{135,000}{1 \times 1,859}\)

\(\Delta \theta = 72.6~ {\textdegree}C\)

The steam started at 100掳C and heats up by 72.6掳C so is now 172.6掳C.

Question

If 0.5 kg of water at 80掳C is changed into steam at 110掳C, how will the energy be used?