Some hot water was added to three times its mass of water at 100 C and the resulting temperature was 200 C. What was the temperature of the hot water?
From ctg ques 2013
Pls explain the answer
Change of temperature by adding water
Re: Change of temperature by adding water
Let, mass of hot water be $m$.
So, mass of water at $100^\circ C$ = $3m$.
Also, suppose, initial temperature of hot water = $\theta$, and, Specific Heat of Water = $\displaystyle s_w$
Now, Heat lost by Hot Water = $ms_w(\theta-200)$, and,
Heat gained by Cold Water = $3ms_w(200-100)=300ms_w$
Since, in a closed system, Heat Lost = Heat Gained.
Therefore, $ms_w(\theta-200)=300ms_w\Rightarrow\theta-200=300\Rightarrow\theta=500^\circ C$.
So, mass of water at $100^\circ C$ = $3m$.
Also, suppose, initial temperature of hot water = $\theta$, and, Specific Heat of Water = $\displaystyle s_w$
Now, Heat lost by Hot Water = $ms_w(\theta-200)$, and,
Heat gained by Cold Water = $3ms_w(200-100)=300ms_w$
Since, in a closed system, Heat Lost = Heat Gained.
Therefore, $ms_w(\theta-200)=300ms_w\Rightarrow\theta-200=300\Rightarrow\theta=500^\circ C$.
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nafistiham
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Re: Change of temperature by adding water
I wonder, why water of $500^\circ C$ or $200^\circ C$ is called water ?
Is it not vapor ?
And, if it is, should we not add the latent heat ?
(Latex edited
)
Is it not vapor ?
And, if it is, should we not add the latent heat ?
(Latex edited
)Last edited by nafistiham on Wed Jan 16, 2013 5:23 pm, edited 2 times in total.
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Re: Change of temperature by adding water
There is some oddity in the wording of the problem.
1. If the situation takes place in normal atmospheric pressure, we should consider the latent heat in calculation. But then the hot water should not be called ‘water’ because it must be steam at obviously more than 200 °C. Also, the linear heat transfer equation may no longer remain valid.
2. On the other hand, with extreme high pressure, it is possible to have the temperature of hot water more than 200 °C, even 500 °C. Again, there is some problem with the language, because we should then call the water ‘supercritical water’, not just hot water. But renaming of water does not solve the mathematical part of the problem. You now have supercritical water and three times that water at same, extreme, high pressure. Unfortunately, the linearity of heat transfer equation is no longer valid at such unusual pressure and temperature.
Therefore, even if we correct the nomenclature in the problem by making some assumptions, this problem still lies within the domain of experimental and empirical science, not fully within theoretical calculation.
1. If the situation takes place in normal atmospheric pressure, we should consider the latent heat in calculation. But then the hot water should not be called ‘water’ because it must be steam at obviously more than 200 °C. Also, the linear heat transfer equation may no longer remain valid.
2. On the other hand, with extreme high pressure, it is possible to have the temperature of hot water more than 200 °C, even 500 °C. Again, there is some problem with the language, because we should then call the water ‘supercritical water’, not just hot water. But renaming of water does not solve the mathematical part of the problem. You now have supercritical water and three times that water at same, extreme, high pressure. Unfortunately, the linearity of heat transfer equation is no longer valid at such unusual pressure and temperature.
Therefore, even if we correct the nomenclature in the problem by making some assumptions, this problem still lies within the domain of experimental and empirical science, not fully within theoretical calculation.
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Prosenjit Basak
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Re: Change of temperature by adding water
These conditions are only possible in a particular air pressure. It must not be possible in normal atmosphere. The air pressure must be high enough to fulfill these conditions.
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