How Much Coolant Do You Need?

A cast-iron engine block of mass m_e with coolant of mass m_c is heated to 100 C ( T_e) in a water bath. The engine block is then quickly submerged in an insulated container holding a mass m_w of 1000 kg of water, at a temperature T_w of 15 C, to find the mass of the coolant in the engine.





The final temperature T_f of the water, engine, and coolant is found to be 18 C after heat from the engine is transferred to the water. The engine coolant used is pure ethylene glycol C_2 H_6 O_2, which has a specific heat c_c of 2.39x10^3 J/(kg C). (Usually you would use a mix of ethylene glycol and water as coolant.) The mass of the engine block used is 275 kg and the specific heat of cast iron c_e is 4.50x10^2 J/(kg C). The specific heat of water c_w is 4187 J/(kg C)


Assume that this is a closed, isolated system.


For this experiment, the students were asked to find the mass of the coolant. If pure ethylene glycol is used as the coolant, what is the mass of coolant m_c used in the experiment in kg

How Much Coolant Do You Need?
Okay, so we know that the engine block and coolant will cool, and the 1000kg of water will warm. The basic idea is that the heat that leaves the hot stuff, MUST be equal to the heat that goes into the cool stuff.


Let Tf be final temp, Let Ti be initial temp





Qh = m_eCe(Tf-100) + m_cCc(Tf-100)or


Qh = (m_eCe+m_cCc)(Tf-100)


note that since Tf %26lt; 100, Qh is negative.





Qc = m_wCw(Tf-15)





so Qc = - Qh


m_wCw(Tf-15) = -(m_eCe + m_cCc)(Tf-100)





You are looking for m_e, so solve for m_e.


Tf = 18