The time taken for a calorimeter containing 75 ~g of water at 62^ C to cool to 58^ C is 9 minutes. When the calorimeter contains 105 ~g of water, it takes 12 minutes to cool from 62^ C to 58^ C . The water equivalent of the calorimeter is

Step-by-step solution

Heat lost =(w+m) C_V d T where, w= water equivalent of calorimeter, m= mass of water, C_V= specific heat of water and d T= temperature difference =T₂-T₁ . Time taken to cool down is proportional to amount of heat lost. Case I 9 minutes Dividing Eq. (i) by Eq. (ii), we get aligned 9 12 & = (75+w) C_V 4^ (105+w) C_V 4^ or 3 (105+w) & =4(75+w) 4 w-3 w & =315 ~g -300 ~g w & =15 ~g aligned