A liuid of mass m and specific heat s is heated to a temperature T. Another liquid of mass `m//2` and specific heat 2s is heated to temperature 2 T. If these two liquids are mixed, the resultant temperature of the nixture will be

Options

A. `(2)/(3)T`
B. `(8)/(5)T`
C. `(3)/(4)T`
D. `(3)/(2)T`

Answer

D

Explanation

Resultant temperature of the mixture,
`T = (m_(1)s_(1)t_(1)+m_(2)s_(@)t_(2))/(m_(1)s_(1)+m_(2)s_(2))`
`implies T_(R)=(msT+ ((m)/(2))(2s)(2T))/(ms+((m)/(2))(2s))`
`implies T_(R)=((1+2)T)/(1+1)`
`therefore T_(R) = (3)/(2)T`