In the above problem mass of ice and water in the mixture when thermal equlibrium is attained is

Options

A. 40 g ice, 180 g water
B. 60 g ice, 160 g water
C. 20 g ice, 200 g water
D. None of the above

Answer

To solve the problem of finding the mass of ice and water in the mixture when thermal equilibrium is attained, we can follow these steps:

### Step 1: Understand the Problem
We need to find the mass of ice and water in a mixture at thermal equilibrium. The problem states that the heat exchange occurs until the system reaches thermal equilibrium.

### Step 2: Identify the Given Data
- The heat absorbed by the ice to melt and then reach thermal equilibrium is given as 8000 calories.
- The latent heat of fusion of ice (L) is approximately 80 calories/gram.
- The initial mass of ice is 120 grams.
- The initial mass of water is 100 grams.

### Step 3: Calculate the Heat Required to Melt the Ice
Using the formula for heat (Q) absorbed during melting:
\[ Q = m \cdot L \]
Where:
- \( Q \) = heat absorbed (calories)
- \( m \) = mass of ice (grams)
- \( L \) = latent heat of fusion (calories/gram)

We can rearrange this to find the mass of ice that can absorb 8000 calories:
\[ 8000 = m \cdot 80 \]
\[ m = \frac{8000}{80} = 100 \text{ grams} \]

### Step 4: Determine the Final Mass of Ice and Water
- Initially, we have 120 grams of ice. After melting 100 grams of ice, we are left with:
\[ \text{Remaining ice} = 120 \text{ grams} - 100 \text{ grams} = 20 \text{ grams} \]
- The water produced from the melted ice will be 100 grams.
- Initially, there was 100 grams of water, so the total mass of water after melting is:
\[ \text{Total water} = 100 \text{ grams (initial)} + 100 \text{ grams (from melted ice)} = 200 \text{ grams} \]

### Step 5: Conclusion
At thermal equilibrium, we have:
- Remaining ice = 20 grams
- Total water = 200 grams

Thus, the total mass of the mixture (ice + water) is:
\[ \text{Total mass} = 20 \text{ grams (ice)} + 200 \text{ grams (water)} = 220 \text{ grams} \]

### Final Answer
The mass of ice and water in the mixture when thermal equilibrium is attained is 220 grams.

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