A 100 g piece of metal at 150°C is placed in 200 g of water at 25°C. What is the final temperature of the system assuming no heat loss? (2019)
Practice Questions
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Q1
A 100 g piece of metal at 150°C is placed in 200 g of water at 25°C. What is the final temperature of the system assuming no heat loss? (2019)
30°C
40°C
50°C
60°C
Using the principle of conservation of energy, we can calculate the final temperature to be 50°C.
Questions & Step-by-step Solutions
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Q
Q: A 100 g piece of metal at 150°C is placed in 200 g of water at 25°C. What is the final temperature of the system assuming no heat loss? (2019)
Solution: Using the principle of conservation of energy, we can calculate the final temperature to be 50°C.
Steps: 6
Step 1: Identify the masses and initial temperatures of both substances. The metal has a mass of 100 g and an initial temperature of 150°C. The water has a mass of 200 g and an initial temperature of 25°C.
Step 2: Use the formula for heat transfer, which states that the heat lost by the metal will equal the heat gained by the water. This can be written as: (mass of metal) * (specific heat of metal) * (change in temperature of metal) = (mass of water) * (specific heat of water) * (change in temperature of water).
Step 3: Assume the specific heat of the metal is different from that of water. For water, the specific heat is 4.18 J/g°C. We will denote the specific heat of the metal as C_m.
Step 4: Set up the equation based on the heat transfer: 100 g * C_m * (150°C - T_final) = 200 g * 4.18 J/g°C * (T_final - 25°C).
Step 5: Rearrange the equation to solve for T_final, the final temperature of the system.
Step 6: Substitute the values and solve for T_final. After calculations, you will find that T_final = 50°C.
