Three liquids with masses m₁,m₂,m₃ are thoroughly mixed. If their specific heats are c₁,c₂

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Three liquids with masses $m_1,m_2,m_3$ are thoroughly mixed. If their specific heats are $c_1,c_2,c_3$ and their temperatures $T_1,T_2,T_3$ respectively, then the temperature of the mixture is

$\frac{{{c_1}{T_1}\, +\, {c_2}{T_2} \,+\, {c_3}{T_3}}}{{{m_1}{c_1}\, +\, {m_2}{c_2} \,+\, {m_3}{c_3}}}$

$\frac{{{m_1}{c_1}{T_1}\, +\, {m_2}{c_2}{T_2} \,+ \,{m_3}{c_3}{T_3}}}{{{m_1}{c_1} \,+\, {m_2}{c_2} \,+\, {m_3}{c_3}}}$

$\frac{{{m_1}{c_1}{T_1} \,+\, {m_2}{c_2}{T_2} \,+\, {m_3}{c_3}{T_3}}}{{{m_1}{T_1} \,+\, {m_2}{T_2} \,+\, {m_3}{T_3}}}$

$\frac{{{m_1}{T_1} \,+\, {m_2}{T_2} \,+\, {m_3}{T_3}}}{{{c_1}{T_1} \,+ \,{c_2}{T_2} \,+\, {c_3}{T_3}}}$

Solution

Let the final temperature be $\mathrm{T}^{\circ} \mathrm{C}$

Total heat supplied by the three liquids in coming down to

$0^{\circ} \mathrm{C}$

$=\mathrm{m}_{1} \mathrm{c}_{1} \mathrm{T}_{1}+\mathrm{m}_{2} \mathrm{c}_{2} \mathrm{T}_{2}+\mathrm{m}_{3} \mathrm{c}_{3} \mathrm{T}_{3}$ $…(i)$

Total heat used by three liquids in raising temperature from $0^{\circ} \mathrm{C}$ to $\mathrm{T}^{\circ} \mathrm{C}$

$=\mathrm{m}_{1} \mathrm{c}_{1} \mathrm{T}+\mathrm{m}_{2} \mathrm{c}_{2} \mathrm{T}+\mathrm{m}_{3} \mathrm{c}_{3} \mathrm{T}$ $…(ii)$

By equating $( i )$ and $(ii)$ we get

$\left(\mathrm{m}_{1} \mathrm{c}_{1}+\mathrm{m}_{2} \mathrm{c}_{2}+\mathrm{m}_{3} \mathrm{c}_{3}\right) \mathrm{T}$

$=\mathrm{m}_{1} \mathrm{c}_{1} \mathrm{T}_{1}+\mathrm{m}_{2} \mathrm{c}_{2} \mathrm{T}_{2}+\mathrm{m}_{3} \mathrm{c}_{3} \mathrm{T}_{3}$

$\Rightarrow \mathrm{T}=\frac{\mathrm{m}_{1} \mathrm{c}_{1} \mathrm{T}_{1}+\mathrm{m}_{2} \mathrm{c}_{2} \mathrm{T}_{2}+\mathrm{m}_{3} \mathrm{c}_{3} \mathrm{T}_{3}}{\mathrm{m}_{1} \mathrm{c}_{1}+\mathrm{m}_{2} \mathrm{c}_{2}+\mathrm{m}_{3} \mathrm{c}_{3}}$

Standard 11

Physics

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normal

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normal

Three liquids with masses $m_1,m_2,m_3$ are thoroughly mixed. If their specific heats are $c_1,c_2,c_3$ and their temperatures $T_1,T_2,T_3$ respectively, then the temperature of the mixture is

Solution

Similar Questions

$540\ g$ of ice at $0\ ^oC$ is mixed with $540\ g$ water at $80\ ^oC$. The final temperature of the mixture is

Two substances $A$ and $B$ of equal mass $m$ are heated at uniform rate of $6\,cal\,s^{-1}$ under similar conditions. A graph between temperature and time is shown in figure. Ratio of heat absorbed $H_A/H_B$ by them for complete fusion is

One kilogram of ice at $0\,^oC$ is mixed with one kilogram of water at $80\,^oC$. Temperature of mixture is …….. $^oC$ (specific heat of water $= 4200\,J\,kg^{-1}\,K^{-1}$ and latent heat of ice $= 336\,KJ \,kg^{-1}$ )

A liquid having coefficient of cubical expansion $\gamma $ is filled in the container having coefficient of linear expansion $\alpha $. If on heating the liquid overflows, then which of the following relations is correct?

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