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 piece 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?

The temperature of the metal is  

Explanation:

From the question we are told that

     The mass of the metal is  

     The specific heat of the metal is  

       The mass of the oil is

       The temperature of the oil is  

       The specific heat of oil is  

       The equilibrium temperature is

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

=>            

Where  the temperature of metal before immersion

The negative sign show heat lost

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

=>        

So  

substituting values

=>      

the part of the wave he is travelling on is the crest