Question

When two different liquids of same mass but at two different temperatures \(27^\circ C\) and \(47^\circ C\) are mixed together, the resulting temperature of the mixture is \(35^\circ C\). The ratio of their specific heat capacities is

• A. 1 : 3
• B. 5 : 3
• C. 3 : 2
• D. 4 : 1
• E. 2 : 7

Hint:

Always check the direction of heat transfer: from higher temperature to lower temperature, ensuring conservation of energy.

Answer 1

The Correct Option is C

Step 1: Let \( c_1 \) and \( c_2 \) be the specific heat capacities of the liquids mixed. Since no heat is lost to the environment, the heat lost by the hotter liquid equals the heat gained by the cooler one. 
Step 2: Set up the equation based on heat transfer: \( m \cdot c_1 \cdot (47 - 35) = m \cdot c_2 \cdot (35 - 27) \). 
Step 3: Simplify to find the ratio \( \frac{c_1}{c_2} = \frac{8}{12} = \frac{2}{3} \). 
Step 4: Thus, the ratio of their specific heat capacities is \( 3:2 \) (inverse of \( \frac{2}{3} \)).