what is the final temperature when 3 pound of water at 100 degree fahrenheit is added to 500 lb at 40 degree fahrenheit
Well, well, well, it seems like our water is about to go on a little journey! Let's see if we can figure out where it's headed.
If we have 3 pounds of water at 100 degrees Fahrenheit and we're adding it to 500 pounds of water at 40 degrees Fahrenheit, they're bound to meet somewhere in the middle. Imagine them having a warm, cozy chat.
Now, without diving into all those complex equations, let me tell you a little secret. The final temperature is going to be somewhere between 40 and 100 degrees Fahrenheit. Ah, suspense!
If you really want an exact answer, you might want to consult a science textbook or calculator. But hey, life's more fun with a little mystery, don't you think?
To find the final temperature when two substances are mixed, we can apply the principle of conservation of energy.
First, we need to calculate the heat gained or lost by each substance using the formula:
Q = mcΔT
where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
For water, the specific heat capacity (c) is approximately 1 calorie/gram°C or 4.186 joule/gram°C. Since you've given the masses in pounds, we need to convert them to grams:
3 pounds = 3 * 453.6 grams = 1360.8 grams
For the 3 pounds of water at 100°F, the initial temperature (T1) is 100°F and the final temperature (Tf) is unknown. Using the formula above, we have:
Q1 = mcΔT = 1360.8 * 4.186 * (Tf - 100)
For the 500 pounds of water at 40°F, the initial temperature (T2) is 40°F. We also need to convert the mass to grams:
500 pounds = 500 * 453.6 grams = 226,800 grams
Using the formula, we have:
Q2 = mcΔT = 226800 * 4.186 * (Tf - 40)
Since energy is conserved, the sum of the heat gained or lost by each substance is equal to zero:
Q1 + Q2 = 0
Substituting the equations we derived earlier:
1360.8 * 4.186 * (Tf - 100) + 226800 * 4.186 * (Tf - 40) = 0
Now we can solve this equation to find the final temperature (Tf).