Thank you for visiting A 39 5 g sample of copper at 99 8 C is carefully placed into an insulated container containing 168 g of water at 18. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
Using the principle of conservation of energy and the specific heat capacities for copper and water, the final temperature when the copper and water reach thermal equilibrium is calculated to be 57.5 °C, which is option C.
Explanation:
To calculate the final temperature when thermal equilibrium is reached between the copper and the water, we'll use the principle of conservation of energy. Specifically, the heat lost by the copper will equal the heat gained by the water since no heat is lost to the surroundings. The amount of heat ( extit{q}) transferred is calculated using the equation extit{q} = m * c * extit{ extDelta T}, where extit{m} is the mass, extit{c} is the specific heat capacity, and extit{ extDelta T} is the change in temperature.
The specific heat capacities for copper and water are 0.385 J/g°C and 4.184 J/g°C, respectively. Setting the heat lost by copper equal to the heat gained by the water we get:
extit{m_{Cu}} * extit{c_{Cu}} * ( extit{T_{final}} - extit{T_{initial,Cu}}) = extit{m_{H2O}} * extit{c_{H2O}} * ( extit{T_{final}} - extit{T_{initial,H2O}})
Plug in the given values:
39.5g * 0.385 J/g°C * ( extit{T_{final}} - 99.8°C) = 168g * 4.184 J/g°C * ( extit{T_{final}} - 18.5°C)
Solving for extit{T_{final}}, we get that the final temperature is option C) 57.5 °C.
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