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Find the equilibrium temperature when equal masses of the first and third are mixed
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Find the equilibrium temperature when equal masses of the first and third are mixed

Find the equilibrium temperature when equal masses of the first and third are mixed-example-1
User EvanGWatkins
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\begin{gathered} Liquid\text{ 1} \\ T_(L1)=10\text{ \degree C} \\ Liquid\text{ 2} \\ T_(L2)=20\text{ \degree C} \\ Liquid\text{ 3} \\ T_(L3)=38\text{ \degree C} \\ For\text{ Liquid 1 and 2} \\ T1=\text{ 12\degree C} \\ Q_(L1)=Q_(L2) \\ mC1(T1-T_(L1))=mC2(T_(L2)-T1) \\ Equal\text{ mass} \\ C1(T1-T_(L1))=C2(T_(L2)-T1) \\ Solving\text{ C1 in term of C2} \\ C1=(C2(T_(L2)-T1))/(T1-T_(L1)) \\ C1=\frac{C2(20\text{ \degree C}-12\text{ \degree}C)}{12\text{ \degree C}-10\text{ \degree C}} \\ C1=4C2 \\ For\text{ Liquid 2 and 3} \\ T2=35.8\text{ \degree C} \\ Q2=Q3 \\ mC2(T2-T_(L2))=mC3(T_(L3)-T2) \\ Equal\text{ mass} \\ C2(T2-T_(L2))=C3(T_(L3)-T2) \\ Solving\text{ C3 in term of C2} \\ C3=(C2(T2-T_(L2)))/(T_(L3)-T2) \\ C3=\frac{C2(35.8\text{ \degree C}-20\text{ \degree C})}{38\text{ \degree C-35.8 \degree C}} \\ C3=7.2C2 \\ For\text{ Liquid 1 and 3} \\ T3=? \\ Q1=Q3 \\ mC1(T1-T_(L1))=mC3(T_(L3)-T2) \\ Equal\text{ mass} \\ C1(T3-T_(L1))=C3(T_(L3)-T3) \\ But \\ C1=4C2 \\ C3=7.2C2 \\ 4C2(T3-T_(L1))=7.2C2(T_(L3)-T3) \\ 4(T3-T_(L1))=7.2(T_(L3)-T3) \\ 4T3-4T_(L1)=7.2T_(L3)-7.2T3 \\ Solving\text{ T3} \\ 4T3+7.2T3=7.2T_(L3)+4T_(L1) \\ 11.2T3=7.2T_(L3)+4T_(L1) \\ 11.2T3=7.2(38\text{ \degree C})+4(10\text{ \degree C}) \\ 11.2T3=273.6\text{ \degree C}+40\text{\degree C} \\ 11.2T3=313.6\text{ \degree C} \\ T3=\frac{313.6\text{ \degree C}}{11.2} \\ T3=28\text{ \degree C} \\ The\text{ equilibrium temperature is 28\degree C} \end{gathered}

Find the equilibrium temperature when equal masses of the first and third are mixed-example-1
Find the equilibrium temperature when equal masses of the first and third are mixed-example-2
Find the equilibrium temperature when equal masses of the first and third are mixed-example-3
User Albanx
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