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A mass m_1 of a substance of specific heat capacity c_1 at tem

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A mass $m_{1}$ of a substance of specific heat capacity $c_{1}$ at temperature $t_{1}$ is mixed with a mass $m_{2}$ of other substance of specific heat capacity $c_{2}$ at a lower temperature $t_{2}$ . Deduce the expression for the temperature of the mixture. State the assumption made, if any.

\frac{m _{1} t _{1} + m _{2} t _{2}}{m _{1} + m _{2}}

\frac{m _{1} t _{1} + m _{2} t _{2}}{m _{1} c _{1} + m _{2} c _{2}}

\frac{m _{1} c _{1} + m _{2} c _{2}}{m _{1} + m _{2}}

\frac{m _{1} c _{1} t _{1} + m _{2} c _{2} t _{2}}{m _{1} c _{1} + m _{2} c _{2}}

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Michael Discussed

A mass

m_{1}

of a substance of specific heat capacity

c_{1}

at temperature

t_{1}

is mixed with a mass

m_{2}

of other substance of specific heat capacity

c_{2}

at a lower temperature

t_{2}

. Deduce the expression for the temperature of the mixture. State the assumption made, if any.

15 mins ago

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Text solutionVerified

Let the temperature of the mixture be

t

let

t_{2} < t < t_{1}

. So the heat supplied by

m_{1}

m_{1} c_{1} (t_{1} - t)

Similarly, the heat absorbed by

m_{2}

m_{2} c_{2} (t - t_{2})

As heat supplied is equal to the heat absorbed. So,

m_{1} c_{1} (t - t_{1}) = m_{2} c_{2} (t_{2} - t) \Rightarrow t = \frac{m _{1} c _{1} t _{1} + m _{2} c _{2} t _{2}}{m _{1} c _{1} + m _{2} c _{2}}

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Question Text	A mass $m_{1}$ of a substance of specific heat capacity $c_{1}$ at temperature $t_{1}$ is mixed with a mass $m_{2}$ of other substance of specific heat capacity $c_{2}$ at a lower temperature $t_{2}$ . Deduce the expression for the temperature of the mixture. State the assumption made, if any.
Answer Type	Text solution:1
Upvotes	150