The heat capacity of a metal is 4200 J/k. Its water equivalent is -

Options

A. 0.5 kg
B. 1 kg
C. 1.5 kg
D. 2 kg

Answer

To find the water equivalent of a metal given its heat capacity, we can follow these steps:

### Step 1: Understand the Definitions
- **Heat Capacity (C)**: The amount of heat required to raise the temperature of a substance by 1 degree Celsius (or 1 Kelvin). It is given as \( C = 4200 \, \text{J/K} \).
- **Water Equivalent (W)**: The mass of water that would absorb the same amount of heat as the substance for the same temperature change.

### Step 2: Relate Heat Capacity to Water Equivalent
The relationship between heat capacity and water equivalent can be expressed as:
\[ W = \frac{C}{S} \]
where \( S \) is the specific heat capacity of water, which is approximately \( 4200 \, \text{J/(kg K)} \).

### Step 3: Substitute the Values
Substituting the values we have:
- \( C = 4200 \, \text{J/K} \)
- \( S = 4200 \, \text{J/(kg K)} \)

Now, substituting these into the equation for water equivalent:
\[ W = \frac{4200 \, \text{J/K}}{4200 \, \text{J/(kg K)}} \]

### Step 4: Calculate Water Equivalent
Now, calculate \( W \):
\[ W = \frac{4200}{4200} = 1 \, \text{kg} \]

### Conclusion
The water equivalent of the metal is \( 1 \, \text{kg} \).

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