The liquids at temperature `60^(@)C` and `30^(@)C` respectively have masses in the ratio 3:4 and their specific heats in the ratio 4:5. The the two liquids are mixed , the resultant temperature is

Options

A. `70^(@)C`
B. `50^(@)C`
C. `40^(@)C`
D. `41.25^(@)C`

Answer

D

Explanation

`S_(1):S_(2)=4:5` `implies (S_(1))/(S_(2))=(4)/(5)` `implies S_(1)=(4S_(2))/(5)`
Resultant temperature,
`t=(m_(1)S_(1)t_(1)+m_(2)S_(2)t_(2))/(m_(1)S_(1)+m_(2)S_(2))`
`implies t=[(3m_(2))/(4)xx(4S_(2))/(5)xx60]+[m_(2)xxS_(2)xx(30)]`
`implies t=(36+30)/(((3)/(5)+1)`
`therefore t= 41.25^(@)C`