Spa Heating...

Discussion in 'Physics' started by Litch, May 28, 2013.

  1. Litch

    Thread Starter Member

    Jan 25, 2013
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    7
    My thermodynamics thesis was lost in the mail - hoping someone can fill in the gaps here...

    So I've read it takes 1kcal to heat 1 litre of water, 1°C.

    My Spa is approx. 1.8m x 1.8m x 0.8m
    V = 2.5 cubic meters
    V = 2500 litres

    We're not going to fill it all the way, and taking into account the curves and inward moulded plastics seats etc... we'll assume the working volume of water is around 2000 Litres.

    Therefore, if I have a Spa with 2,000L of water, which sits at an ambient of around 15°C - to get this up to a nice hot spa (~39°C) I'm going to need to heat it up 24 degrees. So far so good? I'll continue.

    Therefore, the energy required to heat 2,000L of water 24 degrees:

    E = Litres x Δ°C x Energy
    E = 2000L x 24°C x 1kcal
    E = 48,000,000 kcal

    Now to get us in to the electrical domain - since I'm considering an electric element, 1 kcal = 4.18 kJ, therefore:

    E = 48.0Gcal x 4.18
    E = 200,640,000 kJ
    E = ~201 GJ

    And since 1 Joule = 1 Watt for 1 Second,

    E = 201 Gigajoules
    E = 201 Gigawatts for 1 second
    E = 55.8 MW for 1 hour

    Or, using a 3KW element, roughly 2 years. Hang on...

    Now I've obviously gone wrong somewhere, as by that number the amount of energy to heat my spa up in an hour is roughly equivalent to the needs of a small city....

    Help?
     
  2. studiot

    AAC Fanatic!

    Nov 9, 2007
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    How did 2 thousand times 24 times 1 become 48 million?
     
  3. shortbus

    AAC Fanatic!

    Sep 30, 2009
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    Since the 1 has a k after it. :)
     
  4. LDC3

    Active Member

    Apr 27, 2013
    920
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    But the k is still there in the next line. He just made a mistake and put in an extra 1000. :)
     
    shortbus and Litch like this.
  5. LDC3

    Active Member

    Apr 27, 2013
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    Producing 55.8 kW of heat with your 3 kW heater requires more than 18.6 hours (with minimal heat lost). I think you need to add some more heaters. :)
     
  6. Litch

    Thread Starter Member

    Jan 25, 2013
    86
    7
    Thanks LDC3 - I must have read over it a dozen times and didn't pick that up!

    So following on from that,
    E = Litres x Δ°C x Energy
    E = 2000L x 24°C x 1kcal
    E = 48,000 kcal

    Now to get us in to the electrical domain - since I'm considering an electric element, 1 kcal = 4.18 kJ, therefore:

    E = 48.0 Mcal x 4.18
    E = 200,640 kJ
    E = ~201 MJ

    And since 1 Joule = 1 Watt for 1 Second,

    E = 201 MJ
    E = 201 MW for 1 second
    E = 55.8 KW for 1 hour

    Yeah, for 18 hours that would actually never heat up because of the heat loss.

    Or if I had enough insulation around the sides and a hard cover, I may be able to have a spa the next day at that temperature - while using around 70-100KWh of electricity, and with current costs (excuse the pun) at around 25 cents per KWh - that's an expensive spa!

    Back to the drawing board I think, time to look at gas heating solutions, which is about 2 cents per MJ ($4).
     
  7. studiot

    AAC Fanatic!

    Nov 9, 2007
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  8. Dr.killjoy

    Well-Known Member

    Apr 28, 2013
    1,190
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    Are you heating it up with a cover or no cover and what voltage are you using ???



    http://vikingspas.com/owners_oasis/faqs
    5. How long does it take to heat the spa up?
    Our spas that are hooked up 220V will heat up approximately 6-8 degrees/hour. Spas hooked up 110V will heat up approximately 1-2 degrees/hour.
     
  9. Litch

    Thread Starter Member

    Jan 25, 2013
    86
    7
    240v (Mains) - But I don't see how the voltage is relevant in any meaningful way?

    Ah, I see, so that's because they're using the same heating element.

    A heating element is basically a coil of wire - with a certain resistance - say 10Ω

    At 240v, the current flowing through that element is:

    V=IR
    I=V/R
    I=240/10
    I=24Amps

    Power is Volts x Amps

    P ≈ 5.7KW of electrical power is converted to heat, at 240v supply.

    But, if the voltage is dropped to 110v:

    I=V/R
    I=110/10
    I=11A

    And we calculate P:

    P=11 x 110
    P=1.2KW of electrical power is converted to heat at 110v.

    So you can see that the effectiveness of the element they supply will vary substantially with supply voltage - but I don't have a heater element yet, and it doesn't apply to my issue because I'm working purely by power (ignoring voltage). Heater elements over here (Australia) are listed by power, not voltage, because ALL are rated at mains voltage (240v).

    Anyway, because of this feasibility study, the element I get will be used purely for maintaining temperature and I'll be investing in a natural gas spa heater to provide the initial heating from ambient temperature.
     
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