In similar calorimeters, equal volume of water and alcohol, when poured take 100 s and 74 s respectivel to cool from `50^(@)`C to `40^(@)`C. If the thermal capacity of each calorimeter is numerically equal to volume of either liquid, then calculatethe specific heat capacity of alcohol.
(Given, the relative density of alcohol as 0.8 and specific heat capacity of water as 1 `cal/g/^(@)C)`

Options

A. 0.8 cal/`g^(@)`C
B. 0.6 cal/`g^(@)`C
C. 0.9 cal/`g^(@)`C
D. 1 cal/`g^(@)`C

Explanation

b) Let v `cm^(3)` be volume of either liquid
Mass of water = V x 1g
Mass of alcohol = `V xx0.8 = 0.8Vg`
Rate of cooling of the water calrorimeter
`(1/100)V x(50^9@) - 40^(@)`] = `1/5` Vcal/s
Rate of cooling of alcohol calorimeter
`1/74(10V + 8Vs)` cal/s
As, rate of cooling of both is same
`5V = 1/74 ( 10V + 8Vs) rArr s = 0.6` cal/`g^(@)`C