Multiple choice

Two liquids at temperature $60^o$C and $20^o$C respectively have masses in the ratio $3:4$ and their specific heats in the ratio $4:5$. If the two liquids are mixed, the resultant temperature is.

  1. $70^o$C
  2. $50^o$C
  3. $40^o$C
  4. $35^o$C
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D Correct answer
Explanation

Heat lost = Heat gained. m1*c1*(T1 - T) = m2*c2*(T - T2). (3/4) * (4/5) * (60 - T) = 1 * (T - 20). (3/5) * (60 - T) = T - 20. 180 - 3T = 5T - 100. 8T = 280. T = 35.

AI explanation

According to the principle of calorimetry, heat lost by the hotter liquid equals heat gained by the colder liquid, based on the formula mass times specific heat times the change in temperature. Let the masses be 3x and 4x, and the specific heats be 4y and 5y; equating the heat exchanges gives 3x * 4y * (60 - T) = 4x * 5y * (T - 20). Solving the equation 12(60 - T) = 20(T - 20) results in 720 - 12T = 20T - 400, which simplifies to 1120 = 32T, yielding a final temperature of 35 degrees Celsius.

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