In a container of negligible mass 30g of steam at `100^@C` is added to 200g of water that has a temperature of `40^@C` If no heat is lost to the surroundings, what is the final temperature of the system? Also find masses of water and steam in equilibrium. Take `L_v = 539 cal//g and c_(water) = 1 cal//g.^@C.`

Explanation

To solve the problem, we need to find the final temperature of the system when 30 g of steam at 100°C is added to 200 g of water at 40°C, and we also need to find the masses of water and steam in equilibrium.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of steam, \( M_1 = 30 \, \text{g} \)
- Mass of water, \( M_2 = 200 \, \text{g} \)
- Initial temperature of steam, \( T_1 = 100 \, \text{°C} \)
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