# What would be the final temperature of a mixture of 50g of water at 20c temperature and 50g of water at 40c temperature?

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30

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[20+40]/2

because both have the same mass you take the average

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Final temperature:

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The idea of this problem is that the water with the *higher* temperature will lose heat and that the water with the *lower* temperature will gain **the same amount** of heat.

Mathematically, this is expressed as

**lost** by the warmer sample;

**gained** by the cooler sample.

Heat *lost* by a system is **negative**, while heat *gained* by a system is **positive**, hence the minus sign used in the above equation.

The equation that establishes a relationship between heat gained or lost and change in temperature looks like this

So, you mix the two samples together and a thermal equilibrium is reached, meaining that the final temperature will be the same for both samples.

This means that you can write

which is equivalent to

Finally,

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The mixture temperature will be

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M grams of water with M grams of - again water - are mixing. We assume to be waited till the thermodynamic equilibrium is reached. So this means that we expect to measure the same temp

Any system gaining

Let's say M = 50g in this example. Also the specific heats are

canceling and eliminating;

that's

will be the final and thermodynamic equilibrium temperature of the mixture in a steady state manner.

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