What Is the Correct Equation for Equilibrium Temperature 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.

 

[haruspex]

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?

 

[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

 

[haruspex]

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.

 

[Delta2]

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*(T_f - T₁) = m₂*C*(T_f - T₂)

m₁CT_f - m₁CT₁ = m₂CT_f - m₂CT₂

m₁CT_f - m₂CT_f = m₁CT₁ - m₂CT₂
T_f(m₁ - m₂) = m₁T₁ - m₂T₂
T_f = (m₁T₁ - m₂T₂) / (m₁ - m₂)
T_f = (18,750*212 - 187,500*50) / (18,750 - 187,500)
T_f = -5,400,000 / -168,750 = 32 ˚F = 0 ˚C

 

[Delta2]

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]

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.