Thank you for visiting A 30 2 g sample of copper at 99 8 C is carefully placed into an insulated container containing 177 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:
The final temperature when thermal equilibrium is reached is approximately 23.5°C.
Explanation:
When the 30.2 g sample of copper, initially at 99.8°C, is placed into the insulated container with 177 g of water at 18.5°C, heat will transfer from the hot copper to the cooler water until they reach thermal equilibrium. To calculate the final temperature, we can use the principle of conservation of energy, which states that the heat gained by the water will be equal to the heat lost by the copper.
Step 1: Calculate the heat lost by copper:
Q_copper = m_copper * C_copper * ΔT_copper
Where:
m_copper = 30.2 g
C_copper = 0.385 J g⻹°C⻹
ΔT_copper = T_final - T_initial
Step 2: Calculate the heat gained by water:
Q_water = m_water * C_water * ΔT_water
Where:
m_water = 177 g
C_water = 4.184 J g⻹°C⻹
ΔT_water = T_final - T_initial
Step 3: Set the two equations equal to each other and solve for T_final:
m_copper * C_copper * ΔT_copper = m_water * C_water * ΔT_water
Solving for T_final gives us approximately 23.5°C.
In this process, we assume no energy is transferred to or from the container, and we've used the specific heat capacities of copper and water to calculate the final temperature when they reach thermal equilibrium.
Learn more about final temperature:
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