A coil of wire of resistance `50 Omega` is embedded in a block of ice. If a potential difference of 210 V is applied across the coil, the amount of ice melted per second will be

Options

A. `4.12 gm`
B. `4.12 kg`
C. `3.68 kg`
D. `2.625 gm`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Heat Generated in One Second
The heat generated (Q) in one second by the coil can be calculated using the formula:
\[ Q = \frac{V^2}{R} \]
where \( V \) is the potential difference and \( R \) is the resistance.

Given:
- \( V = 210 \, \text{V} \)
- \( R = 50 \, \Omega \)

Substituting the values:
\[ Q = \frac{210^2}{50} \]

### Step 2: Calculate \( 210^2 \)
Calculating \( 210^2 \):
\[ 210^2 = 44100 \]

### Step 3: Substitute Back to Find Q
Now substituting back into the equation for Q:
\[ Q = \frac{44100}{50} = 882 \, \text{J} \]

### Step 4: Convert Heat from Joules to Calories
To find out how much ice can be melted, we need to convert the heat generated from joules to calories. The conversion factor is:
\[ 1 \, \text{calorie} = 4.2 \, \text{J} \]
Thus, to convert joules to calories:
\[ \text{Calories} = \frac{Q}{4.2} \]
Substituting the value of Q:
\[ \text{Calories} = \frac{882}{4.2} \]

### Step 5: Calculate the Number of Calories
Calculating the number of calories:
\[ \text{Calories} = 210 \, \text{calories} \]

### Step 6: Calculate the Mass of Ice Melted
To find the mass of ice melted, we use the fact that it takes 80 calories to melt 1 gram of ice. Therefore, the mass of ice melted (m) can be calculated as:
\[ m = \frac{\text{Calories}}{80} \]
Substituting the value of calories:
\[ m = \frac{210}{80} \]

### Step 7: Calculate the Mass of Ice Melted
Calculating the mass:
\[ m = 2.625 \, \text{grams} \]

### Final Answer
Thus, the amount of ice melted per second is approximately:
\[ \text{Mass of ice melted} \approx 2.625 \, \text{grams} \]

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