The water equivatent of a 400 g copper calorimeter (specific heat `=0.1 "cal"//g^(@)C`)

Options

A. 40 g
B. 4000 g
C. 200 g
D. 4g

Explanation

To find the water equivalent of a 400 g copper calorimeter with a specific heat of 0.1 cal/g°C, we can follow these steps:

### Step 1: Understand the concept of water equivalent
The water equivalent of a substance is the mass of water that would absorb the same amount of heat as the substance for a given temperature change. In this case, we want to find out how much water would have the same heat capacity as the 400 g copper calorimeter.

### Step 2: Write down the formula for water equivalent
The formula for water equivalent (W) can be expressed as:
\[ W = m \cdot s_c \]
where:
- \( m \) = mass of the calorimeter
- \( s_c \) = specific heat of the calorimeter

### Step 3: Substitute the known values
Given:
- Mass of the calorimeter, \( m = 400 \, \text{g} \)
- Specific heat of the calorimeter, \( s_c = 0.1 \, \text{cal/g°C} \)
- Specific heat of water, \( s_w = 1 \, \text{cal/g°C} \)

Using the formula:
\[ W = 400 \, \text{g} \times 0.1 \, \text{cal/g°C} \]

### Step 4: Calculate the water equivalent
Calculating the above expression:
\[ W = 400 \times 0.1 = 40 \, \text{cal/°C} \]

### Step 5: Relate the water equivalent to the mass of water
Since the specific heat of water is 1 cal/g°C, the mass of water that would have the same heat capacity (water equivalent) can be found using:
\[ W = m_w \cdot s_w \]
where \( m_w \) is the mass of water.

Since \( s_w = 1 \):
\[ W = m_w \cdot 1 \]
Thus, \( m_w = W \).

### Step 6: Final calculation
From our previous calculation:
\[ m_w = 40 \, \text{g} \]

### Conclusion
The water equivalent of the 400 g copper calorimeter is **40 grams**.

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