Question

A piece of copper is held in a flame until it reaches thermal equilibrium. The time t takes to reach thermal equilibrium will depend on the thermal capacity of the piece of copper. Then, the piece of copper is transferred quickly to a plastic cup containing water. The thermal capacity of the cup is negligible. The following data are available. 6. Mass of copper Mass of water Rise in temperature of water Final temperature of copper Specific heat capacity of copper390 J kg K-1 Specific heat capacity of water 4200 J kg K-1 -0.12 kg -0.45 kg - 30 K 308 K a. Use the data to calculate the temperature of the flame. b. Explain whether the temperature of the flame is likely to be greater or less than your answer to (a).

Answer 1

Let the initial temp. be \(\mathrm{T}\) (which is also the temp of the flame, approximately).

\(m_{\mathrm{Cu}} c_{\mathrm{Cu}}(T-308)=m_{\mathrm{W}} c_{\mathrm{W}} \Delta T\)

\(T=308+\frac{m_{\mathrm{W}} C_{\mathrm{W}}}{m_{\mathrm{Cu}} c_{\mathrm{Cu}}} \Delta T\)

\(T=308+\frac{0.45 \times 4200}{0.12 \times 390} 30\)

\(T=1211.54 \mathrm{~K}\)

The flame temperature is likely to be higher than because no process is \(100 \%\) efficient, meaning not the copper takes all heat, and thus flame would be at a higher temperature.