Question

Three 107.0-g ice cubes initially at 0°c are added to 0.800 kg of water initially at 21.5°c in an insulated container. (a) what is the equilibrium temperature of the system? °c (b) what is the mass of unmelted ice, if any, when the system is at equilibrium? kg

A) 1.5°C
B) 0.0°C
C) 10.7°C
D) 7.5°C

Answer 1

The question involves physics thermodynamics, seeking to determine the final equilibrium temperature and mass of unmelted ice when ice at 0°C is added to warmer water. The heat transfer between the items must be calculated, potentially involving the specific heat of water and ice, and the latent heat of fusion of ice.

Step-by-step explanation:

The subject of the question is thermodynamics, a branch of physics that deals with heat transfer and temperature changes. We're looking at a scenario where ice at 0°C is added to water at 21.5°C, and we're asked to determine the final equilibrium temperature of the system and the mass of unmelted ice, if any.

To solve this, we apply the principle of conservation of energy: the heat lost by the water as it cools down will be equal to the heat gained by the ice as it warms up (and possibly melts).

The specific heat of water is 4.184 J/g°C, and the specific heat of ice is 2.09 J/g°C. The latent heat of fusion of ice is 334 J/g.

We can set up the equation: (mass of water * specific heat of water * temperature change of water) = (mass of ice * specific heat of ice * temperature change of ice) + (mass of melted ice * latent heat of fusion).

However, since this scenario potentially involves ice melting, we might encounter two possible situations: the ice melts completely, and the final temperature is above 0°C, or some ice remains, and the final temperature is exactly 0°C. Detailed calculations are required to find the correct answer.

Answer 2

The equilibrium temperature of the system is 7.5°C. No unmelted ice is present at equilibrium.

Step-by-step explanation:

To find the equilibrium temperature of the system, we can use the principle of conservation of energy. The heat gained by the water is equal to the heat lost by the ice cubes. Let's calculate the heat gained by the water first:

Q = mcΔT = (0.800 kg)(4186 J/kg·°C)(T_f - 21.5°C)

where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Similarly, the heat lost by the ice cubes is:

Q = mcΔT = (3 × 107.0 g)(2.062 J/g·°C)(T_f - 0°C)

Setting these two equations equal to each other and solving for T_f, we get:

T_f = 7.5°C

For part (b), to determine if there is any unmelted ice at equilibrium, we need to calculate the amount of heat required to melt the ice cubes:

Q = mi_Lf

where mi is the mass of the ice and Lf is the latent heat of fusion. If the amount of heat gained by the water (calculated earlier) is greater than the heat required to melt the ice, then there will be no unmelted ice at equilibrium.

In this case, since the heat gained by the water is greater than the heat required to melt the ice, there is no unmelted ice at equilibrium.