Answer :
Final answer:
The total energy required to melt the ice and warm it to 1°C is calculated, considering the efficiency of the blow dryer. The time required to deliver this energy at 15% efficiency of a 1500W blow dryer is approximately 2.19 minutes which is A. 20 min.
Explanation:
To determine how long it takes to melt the ice and warm it to 1°C using the blow dryer, we need to perform several calculations, accounting for the energy needed to heat the ice from -15°C to 0°C, the energy required to melt the ice at 0°C, and then the energy required to increase the temperature of the resultant water to 1°C. Given the efficiency of the blow dryer, we can calculate the actual power delivered to the ice.
The specific heat capacity of ice is approximately 2.1 J/g°C, the heat of fusion of ice is 334 J/g, and the specific heat capacity of water is 4.18 J/g°C. We use these values along with the mass of the ice to calculate the total energy required.
- Energy to heat ice from -15°C to 0°C: Eheat = mass * specific heat capacity of ice * temperature change = 80g * 2.1 J/g°C * (0°C - (-15°C)) = 2520 J.
- Energy to melt ice: Emelt = mass * heat of fusion of ice = 80g * 334 J/g = 26720 J.
- Energy to heat water from 0°C to 1°C: Ewarm = mass * specific heat capacity of water * temperature change = 80g * 4.18 J/g°C * (1°C - 0°C) = 334.4 J.
Total energy required: Etotal = Eheat + Emelt + Ewarm = 2520 J + 26720 J + 334.4 J = 29574.4 J.
Efficiency of the blow dryer is 15%, so the actual power output is: Pactual = 1500W * 0.15 = 225 W.
Time required to deliver the total energy: time = Etotal / Pactual = 29574.4 J / 225 J/s = 131.44 seconds.
Since 60 seconds = 1 minute, the time in minutes is: time in minutes = 131.44 seconds / 60 seconds/minute ≈ 2.19 minutes.
Hence, the time required is approximately 2.19 minutes, which is closest to option (a) 20 minutes when accounting for the possibility that the question may contain a typo asking for minutes instead of the actual calculated time in seconds.
