# Equilibrium Temp of two fluids

trying_mybest
Homework Statement:
A 5-gallon container of water (1 gal = 3.79 liter) at 212 degrees F is added to 50 gallons of water at 50 degrees F. What is the final equilibrium temperature in degrees C?
Relevant Equations:
Qlost = Qgained
Not really sure how to start this one.

• Delta2

Homework Helper
Gold Member
2022 Award
Homework Statement:: A 5-gallon container of water (1 gal = 3.79 liter) at 212 degrees F is added to 50 gallons of water at 50 degrees F. What is the final equilibrium temperature in degrees C?
Relevant Equations:: Qlost = Qgained

Not really sure how to start this one.
If the final temperature is T degrees F, what are the values of Qlost and Qgained?

• Delta2
trying_mybest
Final temp should be ˚C.

I used m1C∆T1 = m2C∆T2

I keep getting 0 for the final temp when it's supposed to be 18 C

Homework Helper
Gold Member
2022 Award
I keep getting 0 for the final temp when it's supposed to be 18 C
And you'd like someone to guess where you are going wrong?
Final temp should be ˚C.
Yes, but it will be simpler to do one conversion at the end than two at the start.

Homework Helper
Gold Member
Final temp should be ˚C.

I used m1C∆T1 = m2C∆T2

I keep getting 0 for the final temp when it's supposed to be 18 C
That equation looks fine but what do you put for ##\Delta T_1## and ##\Delta T_2##?

trying_mybest
m1 = 5 gal * 3.79 L/gal * 1000 g/L = 18,750 g
m2 = 50 gal * 3.79 L/gal * 1000 g/L = 187,500 g

m1*C*(Tf - T1) = m2*C*(Tf - T2)

m1CTf - m1CT1 = m2CTf - m2CT2

m1CTf - m2CTf = m1CT1 - m2CT2
Tf(m1 - m2) = m1T1 - m2T2
Tf = (m1T1 - m2T2) / (m1 - m2)
Tf = (18,750*212 - 187,500*50) / (18,750 - 187,500)
Tf = -5,400,000 / -168,750 = 32 ˚F = 0 ˚C

Homework Helper
Gold Member
Well, i think the mistake lies right at the start.
$$m_1C(T_f-T_1)=m_2C(T_f-T_2)$$ is not correct, the correct is $$-m_1C(T_f-T_1)=m_2C(T_f-T_2)$$ because one body is losing heat (so the heat will be negative) and the other is gaining heat (so the heat will be positive).

• trying_mybest
trying_mybest
Well, i think the mistake lies right at the start.
$$m_1C(T_f-T_1)=m_2C(T_f-T_2)$$ is not correct, the correct is $$-m_1C(T_f-T_1)=m_2C(T_f-T_2)$$ because one body is losing heat (so the heat will be negative) and the other is gaining heat (so the heat will be positive).

Thank you! I caught that mistake earlier, fixed it, and got the correct answer.

• Delta2