Question

Two liquids \( A \) and \( B \) are at \( 20^{\circ} C \) and \( 50^{\circ} C \) respectively. When equal masses of them are mixed together, the temperature of the mixture becomes \( 26^{\circ} C \). The ratio of specific heat capacities of \( A \) and \( B \) is \( k: 1 \). Find the value of \( k \).

Answer 1

When A and B are mixed then final temperature is 26ºC.

Heat gained by A = Heat lost by B

M_AS_A (26 - 20) = M_BS_B (50 - 26)

\(\because\) M_A = M_B

S_A x 6 = S_B x 24

\(\frac{S_A}{S_B}=\frac{24}6\) 

\(\frac{S_A}{S_B}=\frac41\)

Given \(\frac{S_A}{S_B}=\frac{K}1\)

then \(\frac{K}1=\frac{4}1\) 

K = 4