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

2
by mujeeb
What would be the final temperature of mixture of 50g of water at 20C temperature and 50g of water at 40C temperature?

2015-04-11T23:03:02+05:30

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50 gms water at 20 ⁰ C and 50 gms of water at 40⁰ C are mixed.  Since the masses of the liquid at different temperatures are same, the answer is very easy and simple :  average of 20⁰C and 40⁰C.  that is:  30⁰C.
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final temperature of the mixture =
= [ m1 * T1 + m2 * T2 ] / (m1 + m2)
= [ 50 gms * 20⁰ C + 50 gms * 40⁰C ]  / (50+50)

= 3,000 / 100 = 30⁰C

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another way using specific heats :

let the final temperature be = T ⁰C
Amount of heat given out by the hot water = m * s * (40⁰C - T)
= 50 gms * s* (40 -T)
Amount of heat taken in by the cold water = m * s * (T - 20⁰C)
= 50 gms * s * (T - 20 )

As the amounts are equal, because the heat is transferred from hotwater to the cold water without any loss of heat to any surroundings,
50 * s * (40 -T) = 50 gm * s  * (T-20)
40 - T = T - 20
2 T = 60    => T = 30⁰C
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