How can I save my pet fish by using heat and temperature calculations?

[Maw615]

Hello, this is my first time visiting this forum and I hope someone can help me with my Physics homework. This is the problem:

Your pet fish (Pythagoras) lives in a bowl that holds 4000 ml. of water. The temperature of the water must be at 30° C or Pythagoras will die. Unfortunately, you only have two sources of water. One source of water is at 90° C and the other source of water is at 10° C. Your goal will be to determine how much of each source of water must be added to the bowl so that it contains 4000 ml of 30° C water (so that Pythagoras will live).

Thanks in advance for any help!

 

[Gopi Prashanth]

Remember... M1*C*T1 +

M1 * C * T1 + M2 * C * T2 = (M1 + M2) * C * T3

Cancelling out C...

Remember?

 

[wais]

Hey there! Welcome to the forum.

To solve this problem, we can use the formula Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

First, we need to find the amount of heat that needs to be transferred to the 4000 ml of water to raise its temperature from 10°C to 30°C. We can calculate this by using the specific heat capacity of water, which is 4.18 J/g°C.

Q = (4000 ml) (1 g/ml) (4.18 J/g°C) (30°C - 10°C) = 200,800 J

Next, we need to find the amount of heat that can be transferred from the 90°C water to the 4000 ml of water.

Q = (x ml) (1 g/ml) (4.18 J/g°C) (90°C - 30°C) = 2160x J

Similarly, we can calculate the amount of heat that can be transferred from the 10°C water to the 4000 ml of water.

Q = ((4000 - x) ml) (1 g/ml) (4.18 J/g°C) (30°C - 10°C) = 16640(4000 - x) J

Since we want to have a total of 4000 ml of water at 30°C, we can set up the following equation:

200,800 J = 2160x J + 16640(4000 - x) J

Solving for x, we get x = 1428.57 ml

Therefore, we need to add 1428.57 ml of the 90°C water and (4000 - 1428.57) = 2571.43 ml of the 10°C water to the 4000 ml of water in the bowl to get it to a temperature of 30°C. This will ensure that Pythagoras stays alive.

I hope this helps! Let me know if you have any other questions. Good luck with your homework!