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 (Cu) from 20.0°C to 875.0°C, we will use the formula:

\[ q = m \cdot C \cdot \Delta T \]

where:
- \( q \) = heat absorbed (in Joules)
- \( m \) = mass of the substance (in grams)
- \( C \) = specific heat capacity (in J/g°C)
- \( \Delta T \) = change in temperature (in °C)

### Step 1: Identify the given values
- Mass of copper, \( m = 22.8 \, g \)
- Specific heat capacity of copper, \( C = 0.385 \, J/g°C \)
- Initial temperature, \( T_1 = 20.0 \, °C \)
- Final temperature, \( T_2 = 875.0 \, °C \)

### Step 2: Calculate the change in temperature (\( \Delta T \))
\[ \Delta T = T_2 - T_1 \]
\[ \Delta T = 875.0 \, °C - 20.0 \, °C \]
\[ \Delta T = 855.0 \, °C \]

### Step 3: Substitute the values into the formula
Now we can substitute the values into the heat formula:
\[ q = m \cdot C \cdot \Delta T \]
\[ q = 22.8 \, g \cdot 0.385 \, J/g°C \cdot 855.0 \, °C \]

### Step 4: Perform the calculation
First, calculate \( m \cdot C \):
\[ 22.8 \, g \cdot 0.385 \, J/g°C = 8.763 \, J/°C \]

Now multiply by \( \Delta T \):
\[ q = 8.763 \, J/°C \cdot 855.0 \, °C \]
\[ q = 7500.615 \, J \]

### Step 5: Round the answer
The amount of heat required is approximately:
\[ q \approx 7500.62 \, J \]

### Final Answer:
The amount of heat required to raise the temperature of 22.8 g of copper from 20.0°C to 875.0°C is approximately **7500.62 Joules**.

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