Multiple choice

$0.1 m^{3}$ of water at $ 80 ^ {0}C$ is mixed with $ 0.3 m^{3} $ of water at $ 60 ^{0}C$.The final temperature of the mixture is

  1. $65^{0}C$
  2. $70^{0}C$
  3. $60^{0}C$
  4. $75^{0}C$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the principle of conservation of energy, the heat lost by the hotter water equals the heat gained by the cooler water. Since the specific heat capacity and density of water are constant, the final temperature is the weighted average: (0.1 * 80 + 0.3 * 60) / (0.1 + 0.3) = (8 + 18) / 0.4 = 26 / 0.4 = 65 degrees Celsius.

AI explanation

Using the method of alligation or weighted average, the final temperature equals (V1T1 + V2T2) / (V1 + V2). We substitute the values to get (0.1 multiplied by 80 + 0.3 multiplied by 60) / (0.1 + 0.3). The numerator becomes 8 + 18, which equals 26, and dividing by the total volume of 0.4 gives 65. The final temperature of the mixture is 65 degrees C.

Keep practicing — related questions