Knife blades are often made of hardened carbon steel. The hardening process is a heat treatment in which the blade is first heated to a temperature of 1346 °F and then cooled down rapidly by immersing it in a bath of water. To achieve the desired hardness, after heating to 1346 °F, a blade needs to be brought to a temperature below 5.00 . 102 °F. If the blade has a mass of 0.500 kg and the water is in an open copper container of mass 2.000 kg and sufficiently large volume, what is the minimum quantity of water that needs to be in the container for this hardening process to be successful? Assume the blade is not in direct mechanical (and thus thermal) contact with the container, and neglect cooling through radiation into the air. Assume no water boils but reaches 100 °C. The heat capacity of copper around room temperature is ccopper = 386 J/(kg K). Use the data in the table below for the heat capacity of carbon steel.
Temperature Range (°C) | Heat Capacity (J/kg K) |
150 to 200 | 519 |
200 to 250 | 536 |
250 to 350 | 553 |
350 to 450 | 595 |
450 to 550 | 662 |
550 to 650 | 754 |
650 to 750 | 846 |
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