Multiple choice

Two liquids A and B are at temperatures $75^{o}C$ and $150^{o}C$, respectively. Their masses are in the ratio 2 : 3 and specific heats are in the ratio 3 : 4. The resultant temperature of the mixture, when the above liquids are mixed (neglect the water equivalent of container ) is :

  1. $75^{o}C$
  2. $100^{o}C$
  3. $50^{o}C$
  4. $125^{o}C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the principle of calorimetry (heat lost = heat gained): m1*c1*(T1 - T) = m2*c2*(T - T2). Given m1/m2 = 2/3 and c1/c2 = 3/4, the equation becomes (2/3)(3/4)(75 - T) = (T - 150) is incorrect; rather, (m1*c1)/(m2*c2) = (2*3)/(3*4) = 1/2. So 1*(75 - T) = 2*(T - 150) -> 75 - T = 2T - 300 -> 3T = 375 -> T = 125.