# University of Wisconsin Green Bay

How much energy is required to melt a 2.3 kg block of ice? What is the change in entropy of the ice in this process?

• In this problem, you are asked for energy required to change the state of matter, which just depends on mass and the tabulated value of latent heat. Entropy is defined as the energy in or out of a system (calculated in part a of the problem) divided by temperature. In each case, you aren’t asked for new information in this problem but rather to restate what you know about the situation in a slightly different way.

• There is no need for a picture in most definition problems, and this is one of them. You know (or can look up) melting temperature and latent heat of transformation for ice and are asked for the closely related values of thermal energy and entropy. A picture will not provide any clarity or organization beyond what is already present in the problem.

• In equation form, thermal energy needed to change the state of matter is defined as

Q = mL

and change in entropy is defined as

ΔS = ΔQ/T

These are the only relations you need for this problem.

• Q = mL
Q = (2.3 kg)(334 kJ/kg)
Q = 770 kJ = 770,000 J

ΔS = ΔQ/T
ΔS = (770,000 J)/(273 K)
ΔS = 2800 J/K

There is no further calculation required in this problem.

• Q = mL
Q = (2.3 kg)(334 kJ/kg)
Q = 770 kJ = 770,000 J

ΔS = ΔQ/T
ΔS = (770,000 J)/(273 K)
ΔS = 2800 J/K

This problem is merely a definition problem. You will use the definition of thermal energy in problems that ask, for example, for temperature a change of a system, much as you use Fg = mg as you solve force problems.

Note that the sign on entropy matters. In this case, energy was put into the system to melt the ice (Q is positive) and the entropy increased (ΔS is positive.)