The water equivalent of a copper calorimeter is 4.5g. If the specific heat of copper is 0.09 cal `g^(-1).^(@)C^(-1)`. Then

Options

A. mass of the calorimeter is 0.5 kg
B. Thermal capacity of the calorimeter is 4.5 cal `cal^(@)C^(-1)`
C. heat requried to raise the temperature of the calorimter by `8^(@)C` will be 36 cal
D. heat required to melt 15 gm of ice placed in the calorimeter in equilibrium with ice, will be 1200 cal.

Answer

To solve the problem, we need to determine the thermal capacity of the copper calorimeter, the mass of the calorimeter, the heat required to raise its temperature by a certain amount, and the heat required to melt a specific mass of ice. Let's break it down step by step.

### Step 1: Understanding Water Equivalent
The water equivalent of a calorimeter is the amount of water that would absorb the same amount of heat as the calorimeter for a given temperature change. In this case, the water equivalent of the copper calorimeter is given as 4.5 g. This means that to raise the temperature of the calorimeter by 1°C, we need to provide the same amount of heat as we would to raise the temperature of 4.5 g of water by 1°C.

### Step 2: Calculate Thermal Capacity of the Calorimeter
The thermal capacity (C) of the calorimeter can be calculated using the formula:
\[ C = m \cdot s \]
where \( m \) is the mass and \( s \) is the specific heat. For water, the specific heat \( s_w \) is 1 cal/g°C.

Thus, the thermal capacity of the calorimeter is:
\[ C = 4.5 \, \text{g} \cdot 1 \, \text{cal/g°C} = 4.5 \, \text{cal/°C} \]

### Step 3: Calculate Mass of the Copper Calorimeter
Now, we know that the thermal capacity of the copper calorimeter can also be expressed in terms of its mass and specific heat:
\[ C = m_c \cdot s_c \]
where \( m_c \) is the mass of the copper calorimeter and \( s_c \) is the specific heat of copper (given as 0.09 cal/g°C).

Setting the two expressions for thermal capacity equal gives us:
\[ m_c \cdot 0.09 = 4.5 \]

To find the mass of the calorimeter \( m_c \):
\[ m_c = \frac{4.5}{0.09} = 50 \, \text{g} \]

### Step 4: Heat Required to Raise Temperature by 8°C
To find the heat required to raise the temperature of the calorimeter by 8°C, we can use the thermal capacity we calculated:
\[ Q = C \cdot \Delta T \]
where \( \Delta T \) is the change in temperature.

Thus:
\[ Q = 4.5 \, \text{cal/°C} \cdot 8 \, \text{°C} = 36 \, \text{cal} \]

### Step 5: Heat Required to Melt 15 g of Ice
The heat required to melt ice can be calculated using the formula:
\[ Q = m \cdot L_f \]
where \( L_f \) is the latent heat of fusion of ice (80 cal/g).

For 15 g of ice:
\[ Q = 15 \, \text{g} \cdot 80 \, \text{cal/g} = 1200 \, \text{cal} \]

### Summary of Results
1. Thermal capacity of the calorimeter: **4.5 cal/°C**
2. Mass of the copper calorimeter: **50 g**
3. Heat required to raise the temperature by 8°C: **36 cal**
4. Heat required to melt 15 g of ice: **1200 cal**