Multiple choice

Two liquids of masses $M_1$ and $M_2$ and specific heats $S_1$ and $S_2$ respectively are mixed. The specific heat of the mixture is ____________.

  1. $\cfrac { { { M }_{ 1 }S }_{ 1 }+{ { M }_{ 2 }S }_{ 2 } }{ M_{ 1 }+M_{ 2 } } $
  2. $\cfrac { { { M }_{ 1 }S }_{ 1 }+{ { M }_{ 2 }S }_{ 2 } }{ 2(M_{ 1 }+M_{ 2 }) } $
  3. $\cfrac { { 2({ M }_{ 1 }S }_{ 1 }+{ { M }_{ 2 }S }_{ 2 }) }{ M_{ 1 }+M_{ 2 } } $
  4. $\cfrac { { { M }_{ 1 }S }_{ 1 }-{ { M }_{ 2 }S }_{ 2 } }{ M_{ 1 }+M_{ 2 } } $
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A Correct answer
Explanation

The specific heat of a mixture is the weighted average of the specific heats of the components based on mass: S_mix = (M1*S1 + M2*S2) / (M1 + M2).

AI explanation

The specific heat of a mixture is determined by equating the total heat of the mixture to the sum of the heats of the individual liquids, calculated as mass multiplied by specific heat. This gives the formula (M1 + M2) x S_mixture = (M1 x S1) + (M2 x S2). Dividing both sides by the total mass (M1 + M2) results in the specific heat of the mixture being the weighted average of the individual specific heats: (M1 x S1 + M2 x S2) / (M1 + M2).

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