One piece of copper at 105 degrees Celsius has exactly twice the mass of another

Question

One piece of copper at 105 degrees Celsius has exactly twice the mass of another piece, which is at 45 degrees Celsius. Both pieces are placed inside a calorimeter whose heat capacity is negligible. What is the final temp inside the calorimeter? (C or copper= 0.387 K/g.k )? One piece of copper at 105 degrees Celsius has exactly twice the mass of another piece, which is at 45 degrees Celsius. Both pieces are placed inside a calorimeter whose heat capacity is negligible. What is the final temp inside the calorimeter? (C or copper= 0.387 K/g.k )?

Explanation / Answer

We have two pieces of copper , one is at 105 o C and the other at 45 o C.

let Tf be the final temperature they reach.

Let the mass of the copper at 45 o C is X , then the mass of the copper at 105 o C will be 2X

Heat lost by copper at 105 o C = Heat lost by copper at 45 o C

                       m1C( 105 o c - Tf ) = m2 C (Tf - 45 o c)

                        2X ( 105 o c - Tf ) = X (Tf - 45 o c)[ specific on both sides get cancelled as both are copper]

                                 210oc - 2Tf = Tf - 45oc

                                             3Tf = 255oc

                                             Tf = 85oC

The final temperature will be 85oC

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