First slide

Questions on calorimetry without phase change

Question

Two liquids of equal volume are thoroughly mixed. If their specific heats are $C_{1}, C_{2}$ temperatures $θ_{1}, θ_{2}$ and densities d₁, d₂ respectively, the final temperature of the mixture is:

Moderate

A

$\frac{C_{1} θ_{1} + C_{2} θ_{2}}{d_{1} C_{1} + d_{2} C_{2}}$
B

$\frac{d_{1} C_{1} θ_{1} + d_{2} C_{2} θ_{2}}{d_{1} C_{1} + d_{2} C_{2}}$
C

$\frac{d_{1} C_{1} θ_{1} + d_{2} C_{2} θ_{2}}{d_{1} θ_{1} + d_{2} θ_{2}}$
D

$\frac{d_{1} θ_{1} + d_{2} θ_{2}}{C_{1} θ_{1} + C_{2} θ_{2}}$

Solution

Heat lost = Heat gained
$\Rightarrow {Vd}_{1} C_{1} (θ - θ_{1}) = {Vd}_{2} C_{2} (θ_{2} - θ) \Rightarrow θ = \frac{d_{1} C_{1} θ_{1} + d_{2} C_{2} θ_{2}}{d_{1} C_{1} + d_{2} C_{2}}$

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