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### Specific Heat and Temperature of Mixtures Calculator

Specific Heat and Temperature of Mixtures Equations and Calculator

When substances are mixed the specific heat and temperature of the substances reach an equilibrium on temperature and Specific Heat.

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If w1 lb of a substance at temperature t1 and with specific heat c1 is mixed with w2 lb of a second substance at temperature t2 and with specific heat c2 , provided chemical reaction, heat evolution, or heat absorption does not occur, the specific heat of the mixture is

Eq. 1

${c}_{m}=\frac{{w}_{1}{c}_{1}+{w}_{2}{c}_{2}}{{w}_{1}+{w}_{2}}$

and the temperature of the mixture is

Eq. 2

${c}_{m}=\frac{{w}_{1}{c}_{1}{t}_{1}+{w}_{2}{c}_{2}{t}_{2}}{{w}_{1}{c}_{1}+{w}_{2}{c}_{2}}$

In general,

Eq. 3

${t}_{m}=\frac{\mathrm{\Sigma }wct}{\mathrm{\Sigma }wc}$

To raise the temperature of w1 lb of a substance having a specific heat c1 from t1 to tm, the weight w2 of a second substance required is

Eq. 4

${w}_{2}=\frac{{w}_{1}{c}_{1}\left({t}_{m}-{t}_{1}\right)}{{c}_{2}\left({t}_{2}-{t}_{m}\right)}$

Source:

Marks Standard Handbook for Mechanical Engineers

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