Equal masses of three liquids A, B and C have temperatures 10,^oC , 25,^oC and 40,^oC respectively.

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Equal masses of three liquids $A, B$ and $C$ have temperatures $10\,^oC$, $25\,^oC$ and $40\,^oC$ respectively. If $A$ and $B$ are mixed, the mixture has a temperature of $15\,^oC$. If $B$ and $C$ are mixed then mixture has temperature of $30\,^oC$. If $A$ and $C$ are mixed, the mixture will have a temperature of ........ $^oC$

A

$29$

B

$25$

C

$20$

D

$16$

Solution

$A+B: m S_{A}(15-10)=m S_{B}(25-15)=S_{A}=2 S_{B}$

$\mathrm{B}+\mathrm{C}: \mathrm{mS}_{\mathrm{A}}(30-25)=\mathrm{mS}_{\mathrm{c}}(40-30)=\frac{\mathrm{S}_{\mathrm{B}}}{2}=\mathrm{S}_{\mathrm{e}}$

$A+C: m S_{A}(\theta-10)=m S_{c}(40-\theta)$

$\left(2 S_{B}\right)(\theta-10)=\frac{S_{B}}{2}(40-\theta)$

$4 \theta-40=40-\theta \Rightarrow 5 \theta=80 \Rightarrow \theta=16^{\circ} \mathrm{C}$

Standard 11

Physics

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