A calorimeter contains (0.5 ~kg ) of water at (30^ C ). When (0.3 ~kg ) of water at (60^ C ) is added to it, the resulting temperature is found to be (40^ C ). The water equivalent of the calorimeter is

Step-by-step solution

Temperature of cold water in calorimeter, (T₁=30^ C , m₁=0.5 ~kg =500 ~g ) Temperature of hot water, (T₂=60^ C ), (m₂=0.3 ~kg =300 ~g ) Resulting temperature, (T₃=40^ C ) Let water equivalent of the calorimeter is (W_ gram ). According to principle of calorimetry. Heat lost by warm water (= ) Heat gained by cold water + Heat gained by the calorimeter ( aligned & m₂ (T₂-T₃ )=m₁ (T₃-T₁ )+W (T₃-T₁ ) & 300(60-40)=500(40-30)+W(40-30) & 300 20=500 10+10 W & 6000=5000+10 W & 10 W=6000-5000 10 W=1000 & W=100 ~g = 100 1000