Topic: Thermodynamics
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the block? (specific heat of aluminum: 0.91 J/(g °C))
- A. 50 °C
- B. 206 °C
- C. 103 °C
- D. 227 °C
Answer: C. 103 °C
Explanation: The total power of the drilling machine is 10 kW, but only 50% is used for heating, which equals 5 kW (or 5000 W). The total heat supplied over 2.5 minutes is Q = Power * Time = 5000 W * (2.5 * 60) s = 750,000 J. Using the heat capacity formula Q = m * C * delta_T, we substitute the mass m = 8 kg and specific heat C = 0.91 * 1000 J/(kg °C) = 910 J/(kg °C). This gives 750,000 = 8 * 910 * delta_T. Solving for the temperature change yields delta_T = 750,000 / 7280 ≈ 103.02 °C.