A mass of 50 ~g of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool from 30^ C to 25^ C . A mass of 100 ~g of another liquid in an identical vessel with identical surroundings takes the same time to cool from 30^ C to 25^ C . The specific heat of the liquid is : (The water equivalent of the vessel is 30 ~g .)

Step-by-step solution

As the surrounding is identical, vessel is identical time taken to cool both water and liquid (from 30^ C to 25^ C ) is same 2 minutes, therefore ( dQ dt )_ water = ( dQ dt )_ liquid or, ( m _ W C _ W + W ) T t = ( m _ C _ + W ) T t ( W = water equivalent of the vessel ) or, m _ w C _ w = m _ C _ Specific heat of liquid, C _ = m _ W C _ W m _ = 50 1 100 =0.5 kcal / kg