Question

Three liquids with masses m₁, m₂, m₃ are throughly mixed. If their specific heats are s₁, s₂, s₃ and their temperatures q₁, q₂, q₃ respectively, then the temperature of the mixture is –

• A. $\frac{s_{1}\theta_{1} + s_{2}\theta_{2} + s_{3}\theta_{3}}{m_{1}s_{1} + m_{2}s_{2} + m_{3}s_{3}}$
• B. $\frac{m_{1}s_{1}\theta_{1} + m_{2}s_{2}\theta_{2} + m_{3}s_{3}\theta_{3}}{m_{1}s_{1} + m_{2}s_{2} + m_{3}s_{3}}$
• C. $\frac{m_{1}s_{1}\theta_{1} + m_{2}s_{2}\theta_{2} + m_{3}s_{3}\theta_{3}}{m_{1}\theta_{1} + m_{2}\theta_{2} + m_{3}\theta_{3}}$
• D. $\frac{m_{1}\theta_{1} + m_{2}\theta_{2} + m_{3}\theta_{3}}{s_{1}\theta_{1} + s_{2}\theta_{2} + s_{3}\theta_{3}}$

Answer 1

Answer: (B)

$\frac{m_{1}s_{1}\theta_{1} + m_{2}s_{2}\theta_{2} + m_{3}s_{3}\theta_{3}}{m_{1}s_{1} + m_{2}s_{2} + m_{3}s_{3}}$

Answer 2

Heat gain by (1) = Heat Lost by other

So T_mix = $\frac{m_{1}s_{1}\theta_{1} + m_{2}s_{2}\theta_{2} + m_{3}s_{3}\theta_{3}}{m_{1}s_{1} + m_{2}s_{2} + m_{3}s_{3}}$