Copper metal has a specific heat of 0.385 J/ `g^@C` and has melting point of `1083^@C`. Calculate the amount of heat required to raise the temperature of 22.8 g of Cu from `20.0^@c " to " 875^@C`.

Options

A. `1.97xx10^(-5)J`
B. `1.0xx10^(-2)J`
C. 329 J
D. 7.50 kJ

Answer

To calculate the amount of heat required to raise the temperature of 22.8 g of copper from 20.0 °C to 875 °C, we will use the formula:

\[ Q = M \times C \times \Delta T \]

where:
- \( Q \) is the amount of heat (in joules),
- \( M \) is the mass of the substance (in grams),
- \( C \) is the specific heat capacity (in J/g°C),
- \( \Delta T \) is the change in temperature (in °C).

### Step 1: Identify the given values
- Mass of copper, \( M = 22.8 \, \text{g} \)
- Specific heat of copper, \( C = 0.385 \, \text{J/g°C} \)
- Initial temperature, \( T_i = 20.0 \, \text{°C} \)
- Final temperature, \( T_f = 875 \, \text{°C} \)

### Step 2: Calculate the change in temperature (\( \Delta T \))
\[ \Delta T = T_f - T_i = 875 \, \text{°C} - 20.0 \, \text{°C} = 855 \, \text{°C} \]

### Step 3: Substitute the values into the formula
Now we can substitute the values into the heat equation:
\[ Q = 22.8 \, \text{g} \times 0.385 \, \text{J/g°C} \times 855 \, \text{°C} \]

### Step 4: Perform the calculations
1. First, calculate \( 22.8 \times 0.385 \):
\[ 22.8 \times 0.385 = 8.763 \, \text{J/°C} \]

2. Next, multiply this result by \( 855 \):
\[ 8.763 \, \text{J/°C} \times 855 \, \text{°C} = 7505.055 \, \text{J} \]

### Step 5: Convert joules to kilojoules
To convert joules to kilojoules, divide by 1000:
\[ Q = \frac{7505.055 \, \text{J}}{1000} = 7.505 \, \text{kJ} \]

### Final Answer
The amount of heat required to raise the temperature of 22.8 g of copper from 20.0 °C to 875 °C is approximately **7.50 kJ**.

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