Question

A liquid with 0.48 cal.g^-1.°C^-1 relative heat and 25°C temperature is mixed with another liquid with 0.36 cal.g^-1.°C^-1 and 10°C temparature .If the final temparature is 20°C then in what ratio the liquids are mixed?​

Answer 1

Let the liquids be A and B.

$\huge\underline\mathfrak\color{red}{Given}$

• Relative Heat of the liquid A
• $\sf{ (s _{A} ) = 0.48cal. {g}^{ - 1} . {c}^{ - 1} }$
• Temparature of the liquid A
• $\sf{(t_{A}) = {20}^{0} C }$

$\rule{300}{2}$

• Relative Heat of the liquid B
• $\sf{ (s _{B} ) = 0.36cal. {g}^{ - 1} . {c}^{ - 1} }$
• Temparature of the liquid B
• $\sf{(t_{B}) = {10}^{0} C }$

Final temparature of the liquids=20°C.

$\rule{300}{2}$

$\huge\underline\mathfrak\color{red}{To~Find}$

• The ratio of the liquids.

$\rule{300}{2}$

$\huge\underline\mathfrak\color{red}{Solution}$

Relative Heat of the liquid A

$\sf{ (s _{A} ) = 0.48cal. {g}^{ - 1} . {c}^{ - 1} }$

Temparature of the liquid A

$\sf{(t_{A}) = {20}^{0} C}$

Now,

Relative Heat of the liquid B

$\sf{ (s _{B} ) = 0.36cal. {g}^{ - 1} . {c}^{ - 1} }$

Temparature of the liquid B

$\sf{(t_{B}) = {10}^{0} C}$

After mixing the two liquids, the final temparature of the mixture is 20°C.

Now,

Heat absorbed by A

$\sf{ H_{A}= m_{A} s_{A}(t_{A}- t) } \\ \sf{\implies H_{A}= m_{A} \times 0.48(25 - 20)} \\ \sf{\implies H_{A} = m_{A} \times 0.48 \times 5} \\ \sf{\implies H_{A} = 2.4 m_{A}}$

Heat absorbed by B

$\sf{ H_{B}= m_{B} s_{B}(t - t_{B}) } \\ \sf{\implies H_{A}= m_{A} \times 0.36(20 - 10)} \\ \sf{\implies H_{B} = m_{B} \times 0.36 \times 10} \\ \sf{\implies H_{B} = 3.6 m_{B}}$

$\rule{300}{2}$

According to the fundamental principle of Calorimetry,we get,

$\sf{ H_{A} = H_{B}}$

$\sf{\implies \frac{24 m_{A} }{10} = \frac{36 m_{B} }{10} }$

$\sf{\implies 240 m_{A} = 360 m_{B} }$

$\sf{\implies \frac{ m_{A}}{ m_{B}} = \cancel \frac{360}{240} }$

$\sf{\implies \frac{ m_{A} }{ m_{B} } = \frac{3}{2} }$

$\sf{m _{A}:m_{B} = 3:2}$

Hence, the ratio of the mixed liquids is 3:2.

$\huge\underline\mathfrak\color{red}{Thank~You}$