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Amiraneli [1.4K]
3 years ago
15

An artist working on a piece of metal in his forging studio plunges the hot metal into oil in order to harden it. The metal piec

e has a mass of 60 kg and its specific heat is 0.1027 kcal/(kg · °C). He uses 810 kg of oil at 35°C. The specific heat of oil is 0.7167 kcal/(kg · °C). Once the metal is immersed in the oil, the temperature reaches an equilibrium value of 39°C. How hot was the forged metal piece just before he plunged it into the oil?
Physics
1 answer:
lutik1710 [3]3 years ago
6 0

Answer:

The temperature of the metal is  T_m  =  376.8 ^o C

Explanation:

From the question we are told that

     The mass of the metal is  M =  60 \ kg

     The specific heat of the metal is  c_p  =  0.1027 kcal/(kg \cdot ^oC)

       The mass of the oil is M_o  =  810 \ kg

       The temperature of the oil is  T_o  =  35^oC

       The specific heat of oil is  c_o  =  0.7167 kcal/(kg \cdot ^oC )

       The equilibrium temperature is T_e  =  39 ^oC

According to the law of energy conservation

     Heat lost by metal  =  heat gained by the oil

So  

   The quantity  of heat lost by the metal is mathematically represented as

               Q =  - Mc_p \Delta T

=>            Q =  -Mc_p (T_m  -  T_c)

Where T_ m  the temperature of metal before immersion

The negative sign show heat lost

The quantity  of gained t by the metal is mathematically represented as      

           Q =  M_o c_o \Delta T

=>        Q =  M_o c_o (T_c - T_o)

So  

         Mc_p (T_m  -  T_c)   =   M_o c_o (T_c - T_o)

substituting values

          - 60 * 0.1027 (T_m  - 39)   =   810 * 0.7167 *  (39 - 35)

=>       T_m  =  376.8 ^o C

         

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