The ice skate of a 210-pound hockey player is in contact with the ice over a 2.5mm x 15cm area. Determine the freezing point of the ice under the blade of the skate?
To determine the freezing point of the ice under the blade of the skate, we need to consider the pressure exerted by the hockey player's weight on the ice.
1. Convert the weight of the hockey player from pounds to kilograms:
210 pounds = 210 * 0.4536 = 95.254 kg
2. Convert the area of contact from millimeters square to meters square:
2.5 mm * 15 cm = 2.5 * 0.001 m * 15 * 0.01 m = 0.00375 m^2
3. Calculate the pressure using the formula:
Pressure = Force / Area
The force can be calculated using the weight of the hockey player:
Force = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Hence, the force is given by:
Force = 95.254 kg * 9.8 m/s^2 = 933.6592 N
Now, substitute the force and area into the pressure formula:
Pressure = 933.6592 N / 0.00375 m^2
4. Finally, we need to use the phase diagram of water to determine the freezing point at the given pressure. The freezing point of water decreases with increasing pressure. Therefore, we need to refer to a specific phase diagram for the pressure range of interest.
Since the pressure is relatively low in this scenario compared to extreme conditions, we can assume a typical phase diagram of water, which states that water freezes at 0 degrees Celsius (32 degrees Fahrenheit) under normal atmospheric pressure (101.3 kPa).
Hence, the freezing point of the ice under the blade of the skate will be approximately 0 degrees Celsius (32 degrees Fahrenheit).