Questions: The temperature of a sample of copper increased by 23.5°C when 269 J of heat was applied. Substance Specific heat J /(g · °C) --- --- lead 0.128 silver 0.235 copper 0.385 iron 0.449 aluminum 0.903

Solution Steps

• Temperature increase (\(\Delta T\)) = \(23.5^{\circ} \mathrm{C}\)
• Heat applied (\(q\)) = 269 J
• Specific heat of copper (\(c\)) = 0.385 J/g°C

The formula to calculate the mass of the substance when heat is applied is: \[ q = mc\Delta T \] where \( q \) is the heat applied, \( m \) is the mass, \( c \) is the specific heat, and \( \Delta T \) is the change in temperature.

Rearrange the formula to solve for the mass (\( m \)): \[ m = \frac{q}{c\Delta T} \]

Substitute the given values into the rearranged formula: \[ m = \frac{269 \, \text{J}}{0.385 \, \text{J/g°C} \times 23.5^{\circ} \mathrm{C}} \]

Perform the calculation to find the mass of the copper sample: \[ m = \frac{269}{0.385 \times 23.5} \]

Calculate the denominator: \[ 0.385 \times 23.5 = 9.0475 \]

Divide the heat by the product of specific heat and temperature change: \[ m = \frac{269}{9.0475} \]

Calculate the final result to find the mass of the copper sample: \[ m \approx 29.73 \, \text{g} \]

Final Answer