A calorimeter with negligible heat capacity holds 100 cc of water at 40^ C . In 5 minutes, the water cools to 35^ C . The water is subsequently substituted with an equal volume of K-oil at 40^ C . Determine the time required for the temperature to reach 35^ C given identical surrounding conditions. The specific heat capacities of water and K-oil are 4200 J kg ⁻¹ K ⁻¹ and 2100 J kg ⁻¹ K ⁻¹ , respectively, and the dens

Step-by-step solution

According to Newton's law of cooling, the rate of heat loss is proportional to the temperature difference between the liquid and the surroundings. The rate of heat loss is given by dQ dt = ms dT dt . Since the temperature range and surrounding conditions are identical for both liquids, the average rate of heat loss is the same. Therefore, the time taken to cool is proportional to the total heat capacity of the liquid. t ms Since mass m = V , we have t V s . Given that the volumes are equal, the ratio of the times t