A) \[18.2{}^\circ C\]
B) \[22{}^\circ C\]
C) \[20.2{}^\circ C\]
D) \[25.2{}^\circ C\]
Correct Answer: C
Solution :
| 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 \[{{c}_{B}}\left( 23-19 \right)={{c}_{C}}\left( 28-23 \right)\Rightarrow \frac{{{c}_{B}}}{{{c}_{C}}}=\frac{5}{4}\] |
| \[\Rightarrow \frac{{{c}_{A}}}{{{c}_{C}}}=\frac{15}{16}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,....\left( i \right)\] |
| If \[\theta \] is the temperature when A and C are mixed then, |
| \[{{c}_{A}}\left( \text{ }\!\!\theta\!\!\text{ -12} \right)={{c}_{C}}\left( 28-\text{ }\!\!\theta\!\!\text{ } \right)\Rightarrow \frac{{{c}_{A}}}{{{c}_{C}}}=\frac{28-\text{ }\!\!\theta\!\!\text{ }}{\text{ }\!\!\theta\!\!\text{ -12}}\,\,\,\,...\left( ii \right)\] |
| On solving equations (i) and (ii) \[9=20.2{}^\circ C\] |
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