I have just almost finished plumbing in my bodgy DIY bath and I was wondering how long it takes for the water heater to heat the water in the 50 litre tank by 10°C

I thought for fun instead of doing the back of the cigarette packet calculation I would ask ChatGPT, but just as I was about to do that I thought bollix I will do it myself to keep the rust of my thermodynamics wetware module:

water specific heat capacity = 4.2kj/l.°C

Volume = 50 litres

gives 50 x 4.2 = 200 kj per °C for the whole tank
gives 2000 kj per 10°C for the whole tank

Heater element = 3.5kw = 3.5 kj/s

2000 seconds / 3.5 kj/s = 600 seconds = 10 minutes

The answer is 10 minutes


Then I thought for fun I will just run it past ChatGPT to check

I asked: 'How long does it take to raise 50 litres of water by 10 degrees using a 3.5kw element?'

ChatGPT:

To calculate the time it takes to raise the temperature of water, we can use the following formula:

Q = mcΔT

Where:
Q = the amount of heat energy required (in joules)
m = the mass of the water (in kilograms)
c = the specific heat capacity of water (4.18 J/g°C)
ΔT = the temperature change (in °C)

We know that we need to raise 50 litres of water by 10°C, which is equivalent to 50 kg of water.

So, the amount of heat energy required to raise the temperature of 50 kg of water by 10°C can be calculated as:

Q = (50 kg) x (4.18 J/g°C) x (10°C)
Q = 20900 J

Now, we can use the following formula to calculate the time it takes to generate this amount of heat energy using a 3.5 kW element:

Power = Energy / Time

Where:
Power = 3.5 kW
Energy = 20900 J
Time = the time it takes to generate 20900 J of energy

Solving for time, we get:

Time = Energy / Power
Time = 20900 J / 3500 W
Time = 5.97 seconds

Therefore, it would take approximately 6 seconds to raise 50 litres of water by 10 degrees using a 3.5 kW element. However, this calculation assumes that all the heat generated by the element is absorbed by the water, and there are no other heat losses. In reality, there may be some heat losses to the surroundings, so the actual time may be slightly longer.
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Thick AI

This statement is wrong

Q = (50 kg) x (4.18 J/g°C) x (10°C)
Q = 20900 J

It should read

Q = (50 kg) x (1000g/kg) x (4.18 J/g°C) x (10°C)
Q = 2,090,000 J

The ChatGPT is calculation is off by a factor of 100 which gives it the answer of 6 seconds instead of the correct answer of 600 seconds

It is not even off by the expected amount of 1000 (since it left out the g/kg conversion) but instead off by a mysterious 100

I knew it could get stuff wrong but I am amazed that it gets a basic high school physics question wrong

Although to be fair I was impressed to see it walk through the calculation like it was doing an exam rather than just spit the answer out