Question

The temperatures of equal masses of three different liquids A, B, and C are \(15^\circ C\), \(24^\circ C\), and \(30^\circ C\) respectively. The resultant temperature when liquids A and B are mixed is \(20^\circ C\) and when liquids B and C are mixed is \(26^\circ C\). Then the ratio of specific heat capacities of the liquids A, B, and C is:

• A. 5:8:10
• B. 8:10:5
• C. 5:10:8
• D. 8:5:10

Hint:

The principle of calorimetry states that heat lost = heat gained when two substances mix.

Answer 1

The Correct Option is B

Using the principle of calorimetry: \[ m_A c_A (T_f - T_A) = m_B c_B (T_B - T_f) \] \[ c_A (20 - 15) = c_B (24 - 20) \] \[ 5c_A = 4c_B \] \[ c_A = \frac{4}{5}c_B \] For B and C: \[ c_B (26 - 24) = c_C (30 - 26) \] \[ 2c_B = 4c_C \] \[ c_C = \frac{1}{2} c_B \] Thus, the ratio is: \[ c_A : c_B : c_C = \frac{4}{5} : 1 : \frac{1}{2} \] \[ 8:10:5 \]