- #1
maximus123
- 50
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Hello, my problem is this
It is possible to buy water heaters that provide ‘instant boiling water’ at the turn of a tap. Assume the heater takes in water at 4[itex]^{\circ}[/itex]C and gives out hot water at 100[itex]^{\circ}[/itex] C. Furthermore, assume that the hot water flows out at a rate of 21s[itex]^{-1}[/itex]
How much power is required to heat the water at this rate?
So I have attempted a solution as follows,
Where c is the heat capacity and [itex]\Delta T[/itex] is the temperature difference. My first problem is I wasn't sure what to use for 'c' as I wasn't given a mass for the water. I just used this value from wikipedia for the mass specific heat capacity
So the heat energy required to raise the water by that temperature is
So to get power I multiplied this result by the rate of water flow quoted in the problem giving
But this all seems wrong. I don't know from the question how much mass of water is flowing per second but I have used a mass specific heat capacity. Plus the power seems like a low value. Could anyone point out where I am going wrong?
Thanks a lot
It is possible to buy water heaters that provide ‘instant boiling water’ at the turn of a tap. Assume the heater takes in water at 4[itex]^{\circ}[/itex]C and gives out hot water at 100[itex]^{\circ}[/itex] C. Furthermore, assume that the hot water flows out at a rate of 21s[itex]^{-1}[/itex]
How much power is required to heat the water at this rate?
So I have attempted a solution as follows,
[itex]Q=c\Delta T[/itex]
Where c is the heat capacity and [itex]\Delta T[/itex] is the temperature difference. My first problem is I wasn't sure what to use for 'c' as I wasn't given a mass for the water. I just used this value from wikipedia for the mass specific heat capacity
[itex]c=4.1813 \frac{J}{gK}[/itex]
Obviously [itex]\Delta T=96 [/itex] kelvin
Obviously [itex]\Delta T=96 [/itex] kelvin
So the heat energy required to raise the water by that temperature is
[itex]Q=4.1813 \textrm{ x }96=401.4 \textrm{ J}[/itex]
So to get power I multiplied this result by the rate of water flow quoted in the problem giving
[itex]P=401.4 \textrm{ x }21=8429.5 \textrm{ J}[/itex]
But this all seems wrong. I don't know from the question how much mass of water is flowing per second but I have used a mass specific heat capacity. Plus the power seems like a low value. Could anyone point out where I am going wrong?
Thanks a lot