NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice
A calorimeter of negligible heat capacity contains 100 g water at 40 ° C . The water cools to 35 ° C in 5 m i n . If water is now replaced by a liquid of the same volume as that of water at the same initial temperature it cools to 35 ° C in 2 m i n . Given specific heats of water and liquid are 4200 J k g - 1 ° C - 1 and 2100 J k g - 1 ° C - 1 respectively. Find the density of liquid give the answer in kg m - 3 . [As
Correct answer
8
Step-by-step solution
- d T d t = K 100 × S w T - T 0 ∫ 40 35 − d T T − T 0 = ∫ 0 5 K 100 × S w d t ∫ 40 35 − d T T − T 0 = ∫ 0 2 d t 100 × ρ l s l 5 K 100 S w = 2 K 100 × ρ l s l ρ l = 4 5 g / cm 3 = 4 × 10 − 3 kg 5 × 10 − 6 m 3 = 4 5 × 10 3 = 40 5 × 10 2 = 800   kg / m 3