An experiment is performed to measure the specific heat of copper . A lump of copper is heated in an oven, then dropped into a beaker of water . To calculate the specific heat of copper, the experiment must know or measure the value of all quantities below except the

Options

A. heat capacity of water and breaker
B. original temperature of the copper and the water
C. final (equilibrium) temperature of the copper and the water
D. time taken to achieve equilibrium after the copper is dropped into the water

Answer

To determine the specific heat of copper through the described experiment, we need to understand the various quantities involved in the heat transfer process. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Heat Transfer Process
When the heated copper is dropped into the water, heat will flow from the copper to the water until thermal equilibrium is reached. The heat lost by the copper will be equal to the heat gained by the water (and the beaker).

### Step 2: Identify the Required Quantities
To calculate the specific heat of copper, we need to know:
- The heat capacity of water (C_water).
- The heat capacity of the beaker (C_beaker).
- The initial temperature of the copper (T_initial_copper).
- The initial temperature of the water (T_initial_water).
- The final equilibrium temperature (T_final).

### Step 3: Analyze Each Option
1. **Heat Capacity of Water and Beaker**: This is necessary to calculate the heat gained by the water and the beaker.
2. **Original Temperature of Copper and Water**: This is needed to determine the change in temperature (ΔT) for both substances.
3. **Final Temperature of Copper and Water**: This is also necessary to find ΔT since it helps establish the equilibrium temperature.
4. **Time Taken to Achieve Equilibrium**: This is not required for calculating specific heat because the equation does not depend on the time taken to reach equilibrium.

### Conclusion
The quantity that is not needed to calculate the specific heat of copper is the **time taken to achieve equilibrium**. Therefore, the correct answer is option 4.

### Final Answer
**Option 4: Time taken to achieve equilibrium.**

---