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Heat and Internal Energy and Heat and Temperature Change: Specific Heat Capacity

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Axoren
#1
Nov9-08, 11:42 AM
P: 17
1. The problem statement, all variables and given/known data
When you take a bath, how many kilograms of hot water (49C) must you mix with cold water (12C) so that the temperature of the bath is 36C? The total mass of water (hot plus cold) is 191 kg. Ignore any heat flow between the water and its external surroundings.

Temperature of the Cold Water: 12 C
Temperature of the Hot Water: 49 C
Temperature of the Total Water: 36 C
Mass of the Cold Water: y, 191-x
Mass of the Hotwater: x, 191-y
Mass of the Total Water: 191 kg

2. Relevant equations
Q =mcΔT
Where Q is Joules of Energy, m is Mass of the substance (kg), c is the specific heat coefficient, ΔT is change in Temperature (in Celsius)

3. The attempt at a solution
Total Q = 191 kg * 4186 J/kgC * 36 C
Total Q = 28782936 J
Hot Q = X kg * 4186 J/kgC * 13 C
Cold Q = (191 - X) kg * 4186 J/kgC * 24 C
28782936 J = Hot Q + Cold Q
28782936 J = (X kg * 4186 J/kgC * 13 C) + ((191 - X) kg * 4186 J/kgC * 24 C)
28782936 J = (X kg * 54418 J/kg) + ((191 - X) kg * 100464 J/kg)
28782936 J = 54418X J + 19188624 J - 100464X J
28782936 J = 19188624 J - 46046X J
9594312 J = 46046X J
208.36 kg = X (Answer only needs to be to 2 decimal places)

^This does not make sense, because the mass of the hot water is larger than the mass of the total water. Assistance?
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Andrew Mason
#2
Nov9-08, 01:40 PM
Sci Advisor
HW Helper
P: 6,678
Quote Quote by Axoren View Post
3. The attempt at a solution
Total Q = 191 kg * 4186 J/kgC * 36 C
Total Q = 28782936 J
Hot Q = X kg * 4186 J/kgC * 13 C
Cold Q = (191 - X) kg * 4186 J/kgC * 24 C
28782936 J = Hot Q + Cold Q
28782936 J = (X kg * 4186 J/kgC * 13 C) + ((191 - X) kg * 4186 J/kgC * 24 C)
28782936 J = (X kg * 54418 J/kg) + ((191 - X) kg * 100464 J/kg)
28782936 J = 54418X J + 19188624 J - 100464X J
28782936 J = 19188624 J - 46046X J
9594312 J = 46046X J
208.36 kg = X (Answer only needs to be to 2 decimal places)

^This does not make sense, because the mass of the hot water is larger than the mass of the total water. Assistance?
Total Q = 0 .

So the equation should be [itex]Q_h + Q_c=0[/itex]

AM
Axoren
#3
Nov9-08, 01:41 PM
P: 17
Thank you very much! I don't know how I missed that.

ahef7
#4
Feb12-11, 12:23 AM
P: 2
Heat and Internal Energy and Heat and Temperature Change: Specific Heat Capacity

Hey I really need this answered I've been working on it for 3 hours help.
Question: You want to take a bath with the water temperature at 35.0 degrees C. The water temperature is 38 degrees C from the hot water tap and 11 degrees C from the cold water tap. You fill the tub with a total of 187 kg of water. How many kilograms of water from the hot water tap do you use?
Please help.
ahef7
#5
Feb12-11, 12:36 AM
P: 2
Just kidding i'm stupid. i figured it out... sorry for wasting your time.


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