A 250-g piece of lead is heated to 100ºC and is then placed in a 400-g copper container holding 500 g of water.The specific heat of copper is c = 0.386 kJ/kg · K.The container and the water had an initial temperature of 18.0ºC.When thermal equilibrium is reached,the final temperature of the system is 19.15ºC.If no heat has been lost from the system,what is the specific heat of the lead? (the specific heat of water is 4.180 kJ/kg · K)

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Quizplus · Accepted Answer

The specific heat of lead can be found using the principle of conservation of energy, which states that the heat lost by the lead is equal to the heat gained by the water and the copper container. The formula for heat is $Q = mc\Delta T$, where $m$ is mass, $c$ is specific heat, and $\Delta T$ is the change in temperature.For lead: $Q_{\text{lead}} = m_{\text{lead}}c_{\text{lead}}(T_{\text{final}} - T_{\text{initial, lead}})$For water: $Q_{\text{water}} = m_{\text{water}}c_{\text{water}}(T_{\text{final}} - T_{\text{initial, water}})$For copper: $Q_{\text{copper}} = m_{\text{copper}}c_{\text{copper}}(T_{\text{final}} - T_{\text{initial, copper}})$Given:- $m_{\text{lead}} = 0.250$ kg- $m_{\text{water}} = 0.500$ kg- $m_{\text{copper}} = 0.400$ kg- $c_{\text{water}} = 4.180$ kJ/kg·K- $c_{\text{copper}} = 0.386$ kJ/kg·K- $T_{\text{final}} = 19.15$ºC- $T_{\text{initial, lead}} = 100$ºC- $T_{\text{initial, water and copper}} = 18.0$ºCThe heat lost by the lead is equal to the heat gained by the water and copper:$$m_{\text{lead}}c_{\text{lead}}(19.15 - 100) = m_{\text{water}}c_{\text{water}}(19.15 - 18) + m_{\text{copper}}c_{\text{copper}}(19.15 - 18)$$Solving for $c_{\text{lead}}$:$$c_{\text{lead}} = \frac{m_{\text{water}}c_{\text{water}}(19.15 - 18) + m_{\text{copper}}c_{\text{copper}}(19.15 - 18)}{m_{\text{lead}}(19.15 - 100)}$$Plugging in the given values:$$c_{\text{lead}} = \frac{0.500 \times 4.180 \times (19.15 - 18) + 0.400 \times 0.386 \times (19.15 - 18)}{0.250 \times (19.15 - 100)}$$$$c_{\text{lead}} \approx 0.128 \text{ kJ/kg·K}$$Therefore, the specific heat of lead is approximately 0.128 kJ/kg·K.

A 250-G Piece of Lead Is Heated to 100ºC and Is