Problem: Calorimetry Mass of Water Needed to Cool Engine

[cardsrams82]

Homework Statement

Given the specific heat of water is cw=4180 J/kgC
A 241 kg cast-iron engine contains water as a coolant. Suppose the engine's temperature is 31C when it is shut off and the air temperature is 15C. The heat given off by the engine and water in it as they cool to air temperature is 3.7X10^6 J. (Assume the specific heat of iron is 450 J/kgC)

What mass of water is used to cool the engine? Answer in units of kg.

Homework Equations

Q=mc(deltaT)
Qcold=-Qhot

The Attempt at a Solution

I first try using calorimetry to solve it by setting up an equation but ran into issues since I do not know the initial temperature of water. Any attempt at trying to substiute equations is giving me answers of 1, cancelling out the denominators and such. I then assumed that the combined heat given off (3.7X10^6J) was Q and tried to set the total Q = (MwCw(deltaT)). Again I keep running into the issue that I do not know the initial temperature of the water. I know the combined equilibreum temperate as the entire unit cools to the outside temperature of 15C. I know the heat exerted is 3.7X10^6. I know the mass of the material, the specific heat of both, and the initial temperature of the material. I assume the final heat is the same for both since both the engine and the water cooled to 15C as stated in the problem.What am I doing wrong and how should I go about solving this problem?

 

[denverdoc]

What do we know? We have two materials acting as heat reservoirs.

I suppose you have done collision problems, this is a collision of heat with known final velocity and initial velocities, searching a mass.

 

[cardsrams82]

What do we know? We have two materials acting as heat reservoirs.

I suppose you have done collision problems, this is a collision of heat with known final velocity and initial velocities, searching a mass.

So we have m1 being the water that is holding heat when the engine is running. Then we have the m2 which is the iron engine holding heat until the engine is cooled. I don't see how I have known initial velocities though if I'm not given the initial temperature of the water. I know the amount of heat transferred from the cooling process (or collision process as you state). I know the initial temp or velocity of the heat process from the engine mass. I know the final equilebreum temperature of the two. Isn't the initial water temperature vital in this problem though?

 

[denverdoc]

Good point, the water and the engine must be assumed to be of equal temp.

 

[cardsrams82]

which is where I run into problems, when I assume they have equal initial temps then the answer is incorrect. The problem only states that the engine has an initial temp of 31, it doesn't specify the waters initial temp. You would think with the heat expended you could calculate it.

 

[cardsrams82]

Ok I see what I was doing wrong. I needed to take the Qlost, the heat expended, and set it equal to the total amount of energy which was MwCw(deltaT) + MeCe(deltaT). That gave me Mw=Qlost-MeCe(DeltaT)/Cw(DeltaT)

Thanks for trying though!

 

[denverdoc]

no problem, i should have gone into a little more detail.

But seems like all is well.

 

[cardsrams82]

You were right though, its like a collision event between two heat sources, with Q lost being the total energy exerted by the system and the mass being the variable of interest.