40 kg of cold water was mixed with 16 kg of water at 84 C. What is the initial temperature of cold water if the temperature of the mixture is 34 C.
To find the value of the initial temperature of cold water, we use the equality: Sv * mhol * (tcm – tcm) = Cw * mhor * (tf – tcm); mhol * (tcm – tcm) = mhor * (thot – tcm), whence we express: thol = tcm – mhot * (thot – tcm) / mhol.
Values of variables: tcm – mixture temperature (tcm = 34 ºС); mhot is the mass of hot water (mhot = 16 kg); thot – hot water temperature (thot = 84 ºС); mcold – the mass of cold water (mchol = 40 kg).
Calculation: tcold = tcm – mhot * (thot – tcm) / mcold = 34 – 16 * (84 – 34) / 40 = 14 ºС.
Answer: Cold water had an initial temperature of 14 ºС.
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