An object is heated to 90 degrees Celcius and is then allowed to cool in a room whose air temperature is 25 degrees celcius. If the temperature of the object is 75 degrees celcius after 10 minutes, when will its temperature be 50 degrees celcius?
I have no idea how to do this. There are just to many numbers involved!!
To calculate the time it takes for an object to cool from one temperature to another, we can use Newton's Law of Cooling. According to this law, the rate at which an object's temperature changes is directly proportional to the temperature difference between the object and its surroundings.
Here's the step-by-step process to find the time it takes for the object to cool from 75 degrees Celsius to 50 degrees Celsius:
1. Calculate the temperature difference between the object and its surroundings:
ΔT = 75°C - 25°C = 50°C
2. Determine the time it takes for the object to cool by 1 degree Celsius (let's call it T1):
T1 = 10 minutes (given in the question)
3. Calculate the temperature difference between the object and the desired temperature (75°C - 50°C):
ΔT2 = 25°C
4. Set up a proportion using the ratios of the temperature differences to the time differences:
ΔT1 / T1 = ΔT2 / T2
5. Rearrange the proportion to solve for T2:
T2 = (T1 * ΔT2) / ΔT1
Now, plug in the values:
T2 = (10 minutes * 25°C) / 50°C = 5 minutes
Therefore, it will take approximately 5 more minutes (from the initial 10 minutes) for the object's temperature to reach 50 degrees Celsius.