Latent heat of ice 80 cal/gm . A man melts 60 g of ice by chewing in 1 minute . His power is

Options

A. 4800 W
B. 336 W
C. 1.33 W
D. 0.75 W

Answer

To solve the problem step by step, we need to calculate the power exerted by the man while melting the ice.

### Step 1: Calculate the heat required to melt the ice
The formula for the heat gained by the ice is given by:
\[ Q = m \cdot L \]
where:
- \( Q \) is the heat absorbed,
- \( m \) is the mass of ice,
- \( L \) is the latent heat of fusion.

Given:
- Mass of ice, \( m = 60 \, \text{g} \)
- Latent heat of ice, \( L = 80 \, \text{cal/g} \)

Substituting the values:
\[ Q = 60 \, \text{g} \cdot 80 \, \text{cal/g} = 4800 \, \text{cal} \]

### Step 2: Convert the heat from calories to joules
We know that:
\[ 1 \, \text{cal} = 4.18 \, \text{J} \]

Thus, converting \( Q \) to joules:
\[ Q = 4800 \, \text{cal} \cdot 4.18 \, \text{J/cal} = 20064 \, \text{J} \]

### Step 3: Calculate the time in seconds
The time taken to melt the ice is given as 1 minute. We need to convert this to seconds:
\[ t = 1 \, \text{min} = 60 \, \text{s} \]

### Step 4: Calculate the power exerted by the man
Power is defined as the amount of energy transferred per unit time:
\[ P = \frac{Q}{t} \]

Substituting the values we have:
\[ P = \frac{20064 \, \text{J}}{60 \, \text{s}} \]

Calculating this gives:
\[ P = 334.4 \, \text{W} \]

### Final Answer
The power exerted by the man is approximately \( 334.4 \, \text{W} \).

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