A copper calorimeter of mass 600 gm contains 500 gm of water at temperature of 20^(@)C. A 500 gm of copper block at 100^(@)C is dropped into calorimeter. If the resultant temperature is 25^(0)C, find the specific heat of copper.

A copper calorimeter of mass 600 gm contains 500 gm of water at temper

1.	A copper calorimeter of mass 600 gm contains 500 gm of water at temperature of 20^(@)C. A 500 gm of copper block at 100^(@)C is dropped into calorimeter. If the resultant temperature is 25^(0)C, find the specific heat of copper.
Answer» SOLUTION :Mass of copper calorimeter `(m_(1)) = 300 gm = 0.3` Kg , Specific heat copper = `S_(1)` Change in temp of the calorimeter `= 25 - 20 = 5^(@)C ,` Heat gained by the calorimeter `= m_(1) S_(1)(5) = 0.3 xx S_(1) xx 5 = 1.55_(1)J` Mass of water `(m_(2)) = 500 gm = 0.5` Kg , Specific heat of water `(S_(2)) = 4186 J Kg^(-1)K^(-1)` Change in temp of the water `= 25 – 20 = 5^(@)C` , Heat gained by the water `= m_(2) S_(2)5 = 0.5 xx 4186 xx 5 = 10465J` Mass of the copper block `(m_(3))`= 500 gm = 0.5 Kg, Specific heat of copper `= S_(1)` Change in temp of the block `= 100 – 25 = 75^(@)C` Heat lost by the copper block `m_(3)S_(1) xx 75 = 0.5 xx S_(1) xx 75= 37.5S_(1)J` According to the method of mixtures , Heat lost by copper = Heat gained by the calorimeter + Heat gained by the water `37.5 S_(1) = 1.5 S_(1) + 10465` `369S_(1) = 10465 or S_(1) = (10465)/(36) = 290.7` `therefore" Specific heat of copper "= 290.7 J Kg^(-1)K^(-1.)`