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Potential Energy of an Object at a Height

A liquid of s...

Question

A liquid of specific heat 0.3 at $90^{o} C$ is mixed with another liquid of specific heat 0.5 at $15^{o} C$ . If the final temperature of the mixture is $60^{o} C$ , then find the ratio of masses of the two liquids mixed.

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Solution

$θ = \frac{m_{1} s_{1} θ_{1} + m_{2} s_{2} θ_{2}}{m_{1} s_{1} + m_{2} s_{2}}$

$60 = \frac{m_{1} \times 0.3 \times 90 + m_{2} \times 0.5 \times 15}{m_{1} \times 0.3 + m_{2} \times 0.5}$

$\Rightarrow 6 (3 m_{1} + 5 m_{2}) = 27 m_{1} + 7.5 m_{2}$

$9 m_{1} = 22.5 m_{2}$

$\frac{m_{1}}{m_{2}} = \frac{22.5}{9} = \frac{5}{2}$

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