The amount of ice that will remain when 52g of ice is added to 100 g of water ar 40oc is ..... g at the stage of thermal equabirium at 0oc

To determine how much ice remains when 52 grams of ice is added to 100 grams of water at 40°C, we need to analyze the heat transfer between the water and the ice until thermal equilibrium is reached at 0°C. This involves understanding the concepts of specific heat, latent heat, and the principles of energy conservation.

Understanding the Components

First, let’s break down the components involved in this scenario:

• Ice: Initially at 0°C, it will absorb heat to melt into water.
• Water: Initially at 40°C, it will lose heat as it cools down to 0°C.

Key Concepts

We will use the following concepts to solve the problem:

• Specific Heat of Water: The specific heat of water is approximately 4.18 J/g°C.
• Latent Heat of Fusion: The latent heat required to melt ice is about 334 J/g.

Calculating Heat Transfer

Let’s calculate the heat lost by the warm water and the heat gained by the ice:

Heat Lost by Water

The water will cool from 40°C to 0°C. The heat lost (Q) can be calculated using the formula:

Q = m × c × ΔT

Where:

• m = mass of the water (100 g)
• c = specific heat of water (4.18 J/g°C)
• ΔT = change in temperature (40°C - 0°C = 40°C)

Substituting the values:

Q = 100 g × 4.18 J/g°C × 40°C = 16720 J

Heat Gained by Ice

The ice will absorb heat to melt and then potentially warm up to 0°C. The heat gained by the ice can be calculated in two parts:

• First, the heat required to melt the ice:

Q_melt = m_ice × L_f

Where:

• m_ice = mass of the ice (52 g)
• L_f = latent heat of fusion (334 J/g)

Q_melt = 52 g × 334 J/g = 17368 J

• Since the ice is initially at 0°C, it does not need additional heat to warm up.

Comparing Heat Transfers

Now we compare the heat lost by the water and the heat gained by the ice:

• Heat lost by water: 16720 J
• Heat required to melt the ice: 17368 J

Since the heat lost by the water (16720 J) is less than the heat required to melt all the ice (17368 J), not all the ice will melt.

Calculating the Amount of Ice that Melts

Let’s find out how much ice can actually melt with the available heat from the water:

Using the heat lost by the water:

Q_lost = m_melted_ice × L_f

Rearranging gives:

m_melted_ice = Q_lost / L_f

Substituting the values:

m_melted_ice = 16720 J / 334 J/g ≈ 50.0 g

Final Calculation

Now, we can determine how much ice remains:

Initial mass of ice = 52 g

Mass of ice melted = 50 g

Remaining ice = 52 g - 50 g = 2 g

Conclusion

At thermal equilibrium, when 52 grams of ice is added to 100 grams of water at 40°C, approximately 2 grams of ice will remain at 0°C. This example illustrates the principles of heat transfer and the balance of energy in thermal systems.