Multiple choice

$2$ kg of a liquid at $\displaystyle { 100 }^{ \circ }C$ is poured in a bucket having the same liquid of mass $8$ kg at $\displaystyle { 12 }^{ \circ }C$. Find the final temperature of the mixture when its specific heat capacity is $\displaystyle 130J{ kg }^{ -1 }{ K }^{ -1 }$.

  1. $\displaystyle { 50 }^{ \circ }C$
  2. $\displaystyle { 24.6 }^{ \circ }C$
  3. $\displaystyle { 49.3 }^{ \circ }C$
  4. $\displaystyle { 29.6 }^{ \circ }C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the principle of calorimetry, heat lost by the hot liquid equals heat gained by the cold liquid. Since the specific heat is the same, it cancels out: 2(100 - T) = 8(T - 12). Solving for T gives 200 - 2T = 8T - 96, so 10T = 296, T = 29.6 degrees Celsius.

AI explanation

Using the principle of heat exchange where heat lost equals heat gained, we set 2 * (100 - T) equal to 8 * (T - 12). This simplifies to 200 - 2T = 8T - 96, which further reduces to 10T = 296. The final temperature of the mixture is 29.6 degrees Celsius.

Keep practicing — related questions