Math help #3?

given: specific heat of water





c=4180 J/kg celcius





a 238 kg cast-iron car engine contains water as a coolant.suppose the engine's temperature is 32 celcius when it is shut off and the air temperature is 14 celcius.the heat given off by the engine and water in it as they cool to air temperature is 3.4 x 10 to the sixth J.(assume the specific heat of iron is 450 J/kg celcius)


what mass of water is used to cool the engine? answer in units of kg

Math help #3?
This is a thermo question...





Assume Steady state. This is a control volume problem because mass crosses the boundaries.





First lets define two systems. System 1 will be the iron block along with the water inside. System 2 will be just the iron block. System 3 will be just the coolant in the Iron block.





Due a energy balance for system 2...





SumofQ - W = dU


W = 0


-Q1-Q2 = du


-Q 1-Q2= mC(T2-T1)


Q2=-1{238kg(450 J/kg C)(14-32)+(3.4*10^6 J)}


Q2 = -1.4772E6J





This means 1.4772E6 J of energy is transfer from the iron to the coolant.





Now lets take the coolant inside the iron as the mass (System 3)





W = 0


Q = dU


1.4772E6J = C(T2-T1)


FInd T1





use T1 to find h1.





due energy balance for hole system (System 1)...





Q - W = 0


-3.4E6J - m(h2-h1) = 0


solve for m





I think this is right... I'm not so sure about the energy balance for system 3.