Milk at 19 degrees Celsius is mixed with hot chocolate that is 55 degrees Celsius. What could the temperature of the mixture be?

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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Heat flows from a warmer substance to a colder substance, when in contact and this flow continues till both the substances are at the same temperature. In the given case, heat will flow from the hot chocolate to the colder milk. For simplicity, let us assume that both milk and hot chocolate have the same mass, m and that the final temperature of the milk-hot chocolate combination is T.

Amount of heat lost by chocolate = mass of chocolate x specific heat x change in temperature = m x Sc x (55-T)

Amount of heat gained by milk = mass of milk x specific heat x change in temperature

= m x Sm x (T-19)

Equating the two equations, we get

m x Sc x (55-T) = m x Sm x (T-19)

or, 1.6 (55 -T) = 3.93 (T-19)

Solving this equation, we get T = 29.4 degrees Celsius. 

Hope this helps. 

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