Question

At a fabrication plant, a hot metal forging has a mass of 89.9 kg and a specific heat capacity of 422 J/(kg C°). To harden it, the forging is quenched by immersion in 793 kg of oil that has a temperature of 36.1 °C and a specific heat capacity of 2870 J/(kg C°). The final temperature of the oil and forging at thermal equilibrium is 50.6 °C. Assuming that heat flows only between the forging and the oil, determine the initial temperature in degrees Celsius of the forging.

Answer 1

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Given data:

mass = 89.9 kg

sp. heat capacity = 422 J/kg (Celc)

weight of oil = 793 kg

temperature of oil = 36.1 deg. C

sp. heat capacity = 2870 J/kg

thermal equilibrium = 506 deg C

Solution

Now,  , where m = mass, c = sp. heat, change of temperature

Keep in mind that the heat gained by the oil = the heat lost by the metal

Thus, Heat gained by the oil =

=

and, Heat lost by the metal =

where T = initial temperature and we know that heat lost =

Thus equating both sides we get

so, T= 1010.3288C is the required solution!

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