To determine the heat capacity of the metal object, we need to follow a systematic approach using the information provided in the question. Let's break it down step-by-step. ### Step 1: Understand the Problem We have: - Power of the heater (P) = 2000 W (watts) - Mass of the metal object (m) = 5 kg - Initial temperature (T_initial) = 10°C - Final temperature (T_final) = 10°C + 30°C = 40°C - Time (t) = 10 minutes = 10 × 60 seconds = 600 seconds ### Step 2: Calculate the Total Energy Supplied The energy (Q) supplied by the heater can be calculated using the formula: \[ Q = P \times t \] Where: - \( Q \) is the energy in joules (J) - \( P \) is the power in watts (W) - \( t \) is the time in seconds (s) Substituting the values: \[ Q = 2000 \, \text{W} \times 600 \, \text{s} = 1,200,000 \, \text{J} \] So, the total energy supplied to the metal object is 1,200,000 J. ### Step 3: Calculate the Temperature Change The temperature change (ΔT) is: \[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 40°C - 10°C = 30°C \] ### Step 4: Use the Heat Capacity Formula The heat capacity (C) of the material can be calculated using the formula: \[ Q = m \times C \times \Delta T \] Where: - \( Q \) is the heat energy supplied (in joules) - \( m \) is the mass of the object (in kg) - \( C \) is the heat capacity (in J/°C) - \( \Delta T \) is the change in temperature (in °C) Rearranging the formula to solve for C gives: \[ C = \frac{Q}{m \times \Delta T} \] ### Step 5: Substitute the Values Now, substituting the known values into the equation: \[ C = \frac{1,200,000 \, \text{J}}{5 \, \text{kg} \times 30 \, \text{°C}} \] Calculating the denominator: \[ 5 \, \text{kg} \times 30 \, \text{°C} = 150 \, \text{kg°C} \] Now substituting this back into the equation for C: \[ C = \frac{1,200,000 \, \text{J}}{150 \, \text{kg°C}} = 8000 \, \text{J/°C} \] ### Final Answer Thus, the heat capacity of the material is: \[ C = 8.0 \times 10^3 \, \text{J/°C} \] ### Explanation of Options - **Option A: 6.0 x 10^4 J/°C** - This value is too high and does not match our calculated heat capacity. - **Option B: 4.0 x 10^4 J/°C** - This value is also too high and does not correspond to our calculations. - **Option C: 1.2 x 10^4 J/°C** - This value is incorrect as it does not match the calculated heat capacity. - **Option D: 8.0 x 10^3 J/°C** - This is the correct answer, as it matches our calculation. ### Common Pitfalls - **Misunderstanding Units**: Ensure that you convert time into seconds when using the power in watts. - **Forgetting to Calculate ΔT**: Always remember to find the change in temperature correctly. - **Incorrect Rearrangement of Formulas**: Be careful when rearranging formulas to avoid mistakes. ### Revision Summary - The energy supplied by the heater is calculated using \( Q = P \times t \). - The temperature change is found by subtracting the initial temperature from the final temperature. - The heat capacity is calculated using \( C = \frac{Q}{m \times \Delta T} \). - The correct answer for the heat capacity of the material is \( 8.0 \times 10^3 \, \text{J/°C} \).