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Question

In a factory, various metal cylinders are forged and then plunged into a liquid to quickly cool the metal. The metal pieces vary in mass, and are produced at a temperature of 572
degrees Fahrenheit [°F]. The liquid used to cool the metal is glycerol. The initial temperature of glycerol is 20
degrees Celsius [°C]. At the end, glycerol and the metal will be at the
same temperature. Determine the final temperature of the metal and the glycerol in units of degrees Fahrenheit [°F].

The final temperature of cadmium is................°F. (Round your answer to three significant digits.)

Answer 1

I will explain how to solve this, but YOU look up the needed data and do the math.

 

m = mass of the hot metal

c_h = specific heat of the metal

T_h = initial temperature of the hot metal

T_e = final equilibrium temperature of the metal and the liquid it is immersed in

M = mass of the cool liquid

c_l = specific heat of the liquid

T_l = initial temperature of the cool liquid

 

Conservation of energy requires that

 

mc_h(T_h - T_e) = Mc_l(T_e - T_l)

 

You need to know the masses of the metals (m) and the glycerol (M).  You were given T_h = 572°F and T_l = 20°C.  You need to look up the specific heats of the metals (c_h) and glycerol (c_l), which should be in tables in your engineering textbook.  Plug the numbers into the equation above, and then solve for the equilibrium temperature T_e.  Be very careful working with the units.  You will need data in compatible units, unless you also want to convert units, which can be very tedious.