A) \[18.2{}^\circ C\]
B) \[22{}^\circ C\]
C) \[20.2{}^\circ C\]
D) \[25.2{}^\circ C\]
Correct Answer: C
Solution :
[c] Heat gain = heat lost \[{{C}_{A}}\left( 16-12 \right)={{C}_{B}}\left( 19-16 \right)\Rightarrow \frac{{{C}_{A}}}{{{C}_{B}}}=\frac{3}{4}\] and\[{{C}_{B}}\left( 23-19 \right)={{C}_{C}}\left( 28-23 \right)\Rightarrow \frac{{{C}_{B}}}{{{C}_{C}}}=\frac{5}{4}\] \[\Rightarrow \frac{{{C}_{A}}}{{{C}_{C}}}=\frac{15}{16}\] ?(i) If\[\theta \] is the temperature when A and C are mixed then, \[{{C}_{A}}(\theta -12)={{C}_{C}}(28-\theta )\] \[\Rightarrow \frac{{{C}_{A}}}{{{C}_{C}}}=\frac{28-\theta }{\theta -12}\] ?(ii) On solving equations (i) and (ii) \[\theta = 20.2{}^\circ C\]
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