Question

2.0 kg of solid gold (Au) at an initial temperature of 1000K is allowed to exchange heat with 1.5 kg of liquid gold at an initial temperature at 1336K. The solid and liquid can only exchange heat with each other. What kind of analysis do you need to perform in order to determine whether, once thermal equilibrium is reached, the mixture will be entirely solid or in a mixed solid/liquid phase?

Answer 1

The question involves a thermodynamic analysis using heat transfer and phase change principles to determine if a mixture of solid and liquid gold will become entirely solid or remain mixed upon reaching thermal equilibrium.

Step-by-step explanation:

To determine whether the mixture of 2.0 kg of solid gold at 1000K and 1.5 kg of liquid gold at 1336K will be entirely solid or in a mixed solid/liquid phase upon reaching thermal equilibrium, a thermodynamic analysis involving the principles of heat transfer and phase change is required. This analysis will utilize the concept of conservation of energy, accounting for the specific heats of solid and liquid gold as well as the latent heat of fusion if a phase change occurs. The calculations will involve setting the heat lost by the liquid gold equal to the heat gained by the solid gold until both reach the same temperature. If the final temperature is below the melting point of gold without all the solid gold melting, the result will be a mixture. If all the solid melts before reaching the equilibrium temperature, the final state will be all liquid. It's critical to remember that the process must comply with the melting point of gold, which is 1064K.

Answer 2

Step-by-step explanation:

The specific heat of gold is 129 J/kgC

It's melting point is 1336 K

It's Heat of fusion is 63000 J/kg

Assuming that the mixture will be solid, the thermal energy to solidify the gold has to be less than that needed to raise the solid gold to the melting point. So,

The first is E1 = 63000 J/kg x 1.5 = 94500 J

the second is E2 = 129 J/kgC x 2 kg x (1336–1000)K = 86688 J

Therefore, all solid is not correct. You will have a mixture of solid and liquid.

For more detail, the difference between E1 and E2 is 7812 J, and that will melt

7812/63000 = 0.124 kg of the solid gold