Equal volumes of water and alcohol when put in similar calorimeters take `100 sec` and `74 sec` respecively to cool from `50^(@)C` to `40^(@)C`. The thermal capacity of each calorimeter in numerically equal to the volume of either liquid. The specific gravity of alcohol is `0.8` if the specific heat capacity of water is `1 cal//gm`, the specific heat capcity of alcohol will

Options

A. `0.7cal//g^(@)C`
B. `0.8cal//g^(@)C`
C. `1.6cal//g^(@)C`
D. `1.8cal//g^(@)C`

Explanation

Applying newton's low on water calorimeter
`(m_(1)s_(1)+m_(2)s_(2))(dT)/(dt)=kA(T-T_(0))`
`[(rhov1)+v)]((50-40)/(100))=kA(45-T_(0))`
`[(0.8rho)vS+v)[(50-40)/(74)]=kA(45-T_(0))`
using `rho=1gm//cm^(3)` by solving `S=0.6cal//gm^(@)C`