A calorimeter of negligible heat capacity contains `100cc` of water at `40^(@)C` . The water cools to `35^(@)C` in `5` minutes. The water is now replaced by k-oil of equal volume at `40^(@)C` . Find the time taken for the temperature to become `35^(@)C` under similar conditions. Specific heat capacities of water and K-oil are `4200Jkg^(-1)K^(-1)` and `2100Jkg^(-1)K^(-1)` respectively. Density of K-oil `=800kgm^(-3)` .

Answer

B

Explanation

From the law of cooling we have
`(35 -T_(0)) = (40 -T_(0))e - ((kt)/(rhosV))`
Since the intial and the final temperature differences are the same, we must have `rho_(1) S_(1) t_(2) =rho_(2) S_(2) t_(1)`
`:. T_(2) (800xx 2100 xx 5)/(1000 xx 4200) =2min`
As the properties of the exponential functions demand in equal intervals of time the fall in the temperature difference' has the same ratio .