A drilling machine of 5 kW is used to drill a hole in the block of copper of mass 4.0 kg. Calculate the rise in temperature of the block in 5 minutes if 75% of the energy is used in heating the block. Given specific heat of copper = 0.385 J/g°C.

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480.09°C

234.22°C

730.52°C

82.45°C

answer is C.

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Detailed Solution

Explanation

Step 1: Calculate Total Energy Supplied

Power: 5 kW = 5000 W
Time: 5 minutes = 5 × 60 = 300 seconds
Total Energy Supplied:
Total Energy = Power × Time
Total Energy = 5000 W × 300 seconds = 1,500,000 J

Step 2: Calculate Energy Used for Heating

Efficiency: 75% = 0.75
Energy Used for Heating:
Energy = Total Energy × Efficiency
Energy = 1,500,000 J × 0.75 = 1,125,000 J

Step 3: Calculate the Temperature Rise

Mass of Copper: 4.0 kg = 4000 g
Specific Heat of Copper: 0.385 J/g°C
Formula: ΔT = Energy Used / (Mass × Specific Heat)
Substituting the values:
ΔT = 1,125,000 J / (4000 g × 0.385 J/g°C)
ΔT = 1,125,000 J / 1540 J/°C
ΔT ≈ 730.52°C

Final Answer

The rise in temperature of the copper block is approximately 730.52°C.

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