A liquid of specific heat 0.5 at 60^(@)C, is mixed with another liquid of specific heat 0.3 at 20^(@)C. After mixing, the temperature of the mixture becomes 30^(@)C. In what proportion by weight are the liquids mixed ?

A liquid of specific heat 0.5 at 60^(@)C, is mixed with another liquid

1.	A liquid of specific heat 0.5 at 60^(@)C, is mixed with another liquid of specific heat 0.3 at 20^(@)C. After mixing, the temperature of the mixture becomes 30^(@)C. In what proportion by weight are the liquids mixed ?
Answer» Solution :Mass of liquid `A = m_(1)` , Mass of heat liquid `B = m_(2)` , Specific heat of `A(S_(1)) = 0.5` Specific heat of `B(S_(2)) = 0.3` , Temperature of `A(t_(1)) = 60^(0)C` , Temperature of `B(t_(2)) = 20^(0)C` Final temperature `(t) = 30^(0)C` , Fall in temperature of `A = 60 - 30 = 30^(0)C` RISE in temperature of `B = 30 - 20 = 10^(0)C` Heat lost by the liquid `A = m_(2)S_(1) (t_(1) - t) = m_(1) xx 0.5 xx 30` CAL Heat gained by the liquid `B = m_(2) S_(2) (t-t_(2)) = m_(2) xx 0.3 xx 10` cal Heat lost by the liquid A = heat gained by the liquid B `m_(1) xx 0.5 xx 30 = m_(2) xx 0.3 xx 10 (or) (m_(1))/(m_(2))=(0.3xx10)/(0.5xx30) = 1/5 = 1:5`.