Hot Water
Hot Water
How much hot water is needed to bring the bath back to its original temperature?
A bath is filled up with hot water, say 42 degrees C. A volume of cold water is added, taking the temperature down to 38 degrees C.
As a proportion of the water that is already in the bath, how much hot water (42 degrees C) will be needed to bring the whole bath back up to 42 degrees C.
If you could show your working and explain any laws you are using that would be great.
Use Q=mcθ
where Q=energy in Joules
m=mass in kg
c=specific heat capacity, unit is J/[(kg)(℃)]
specific heat capacity of water is 4200 (around that)
temperature change is 4 deg
assume mass of water at first is 100g.
assuming no heat loss, the loss of heat in the water of 42deg = gain of heat in the water of 38 deg.
thus Q1 = Q2.
(100)(4200)(4)=(4200)(4)m
m=0.01g
thus the total mass of water now is 100.001g.
now, to pour 42deg water to bring it up to 42deg.
Q1=Q2
m1c1θ1=m2c2θ2
(100.001)(4200)(4)=m(4200)(0)–>no change in temp. stay at 42
thus, m=[(100.001)(4200)(4)]/[(4200)(0)]
the answer is undefined , ∞
therefore, the amount of water is undefined, or rather, infinity. impossible to bring it back up to 42 deg with water of temp 42 deg.
remember, eqn is Q=mcθ
where Q=energy in Joules
m=mass in kg
c=specific heat capacity, unit is J/[(kg)(℃)]
Which freezes faster, hot or cold water. A Science Experiment from Mr. Herbert
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