I am having a hard time solving this problem. The formula given is:
T=Tin - (Tin - Tinit.)e(-v/v)t
If the initial temperature Tinit is 115 (degrees F), the cold water temperature is 35 (degrees F) (1.7 degrees C), and the volume and volumetric flow rate are 3,000 liters and 30 liters per minute, respectively,
(a) Calculate the expected water temperature at 5-minute intervals for the first 60 seconds after the flow of cold water is established;
See your post above.
To solve this problem, we need to substitute the given values into the formula and calculate the expected water temperature at 5-minute intervals for the first 60 seconds. Let's break it down step by step:
Step 1: Understand the given values
- Tinit = 115 degrees F (initial temperature)
- Tin = 35 degrees F (cold water temperature)
- v = 30 liters per minute (volumetric flow rate)
- t = time in minutes
Step 2: Calculate the value of e(-v/v)
- In the formula, we have e(-v/v). The value of e is approximately 2.71828.
- We can calculate e(-v/v) as e^(-1).
Step 3: Calculate the expected water temperature using the formula
- T = Tin - (Tin - Tinit)e(-v/v)t
- We will consider time intervals of 5 minutes for the first 60 seconds, which means t = 0, 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60 seconds.
Let's calculate the expected water temperature for each time interval:
For t = 0 seconds:
- T = 35 - (35 - 115)e(-1)^(0/30)
- T = 35 - 80e^0
- T = 35 - 80(1)
- T = 35 - 80
- T = -45 degrees F
For t = 5 seconds:
- T = 35 - (35 - 115)e(-1)^(5/30)
- T = 35 - 80e^(-1/6)
- T = 35 - 80(0.839)
- T = 35 - 67.12
- T = -32.12 degrees F
Similarly, calculate the expected water temperature for each 5-minute interval until t = 60 seconds.
By following these steps, you can calculate the expected water temperature at 5-minute intervals for the first 60 seconds after the flow of cold water is established.