During exercise, a person may give offf 180 kcal of heat in 30 min by evaporation of water from the skin. How much water has been lost? Given that latent heat of vaporization of water is 540 cal/gm.

Answer

To find out how much water has been lost due to evaporation when a person gives off 180 kcal of heat, we can follow these steps:

### Step 1: Convert the heat released from kcal to cal
Given that 1 kcal = 1000 cal, we can convert 180 kcal to calories:
\[ 180 \text{ kcal} = 180 \times 1000 \text{ cal} = 180,000 \text{ cal} \]

### Step 2: Identify the latent heat of vaporization
The latent heat of vaporization of water is given as 540 cal/gm. This means that to vaporize 1 gram of water, 540 calories of heat are required.

### Step 3: Calculate the amount of water vaporized
To find the mass of water that has evaporated, we can use the formula:
\[ \text{Mass of water (g)} = \frac{\text{Total heat released (cal)}}{\text{Latent heat of vaporization (cal/g)}} \]
Substituting the values:
\[ \text{Mass of water} = \frac{180,000 \text{ cal}}{540 \text{ cal/g}} = \frac{180,000}{540} \]

### Step 4: Perform the division
Calculating the above expression:
\[ \text{Mass of water} = \frac{180,000}{540} \approx 333.33 \text{ g} \]

### Conclusion
Therefore, the amount of water lost due to evaporation is approximately **333.33 grams**.

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