Quiz - Physics - Water and Heat

[scubadada]

I did a similar calculation to that of @saxman242 typing while he was posting:

The thermal conductivity of water is 0.6 and that of air is 0.025 W/(m·K), 24 times greater. The PADI Encyclopedia of Recreational Diving says 20 times. We'll have to wait until PB lets us know which answer is "correct", I think I know how this will turn out

 

[tursiops]

Gotta love it. Everybody is using their own definitions of things to show that PADI is full of it. Jeez.

The heat capacity of water is around 4200 J/kg-K

The heat capacity of air, at standard pressure and temp (which is realistic for most of the diving we do... standard pressure is at sea level) is around 1000 J/kg-K

So of course 4200 is not "thousands" of times greater than 1000.

Again a question based on a wrong physical explanation. The thermal conductivity of water is larger than air, but this is not BECAUSE the heat capacity of water is approximately 4 times larger than that of air. 4 times, not thousands times !!!
Heat capacity and thermal conductivity are two entirely independent concepts.

Heat capacity can be expressed in many ways; these two posts have chosen per unit mass, perhaps to show that PADI is wrong. But PADI has used the heat capacities per unit volume, which is where they get their "thousands of time greater" from. And, per unit volume is more relevant for the application....we as divers are surrounded by about the same volume of air as water....it is not the mass ratios that are relevant.

Thermal conductivity of sea water is temperature and salinity dependent, but if we assume 20c water with a salinity of 25 g/kg, the thermal conductivity is .6 W/m-K
For air at 26c, thermal conductivity is .026 W/m-K. Given those conditions, the thermal conductivity of water is 23 times higher.

Right on.

The PADI problem here is trying to keep it simple. They do have a tendency to step in it from that desire. Angelo is quite correct that heat capacity and thermal conductivity are different concepts...the former is about storing the heat, the latter is about moving the heat.

LECTURE FOLLOWS...
For the diver, the issue is whether you get cold or not. You get cold if you lose heat. You lose heat if your stored heat can easily be transported away from you.....that is a heat transfer problem, which requires there to be a temperature difference between you and what is around you, and a way to move the heat. That heat can be moved by conduction, convection, and radiation. The latter is a tiny amount and can be ignored except in the sales literature from some wetsuit manufacturers that claim their suit reflects the heat back toward your body; this might be true, but is such a small amount it matters not. Conduction and convection are the big terms in heat transfer for divers. Convection is usually much more efficient that conduction, but we divers try and mitigate it with exposure suits.....even rash guards will help. Conduction is the term we cannot mitigate very well, but a layer of air between us and the water is very helpful....because the air has low thermal conductivity and poorly moves heat from us to the surroundings. A drysuit works this way. But a wetsuit is different; it fills with water, which easily transfers our heat to the neoprene, so it is the neoprene that has the poor thermal conductivity and keeps our heat from getting lost to the surrounding water. Neoprene is actually a foam composed of air (or nitrogen) bubbles and rubber. The thermal conductivity of the rubber/air mixture (say, 5mm neoprene) is typically a number like 0.05 W/m-K, or twice the thermal conductivity of air but still a lot less than that of water. A wetsuit helps keep you warm so long as it does not allow water to be circulating into and out of it.

 

[Angelo Farina]

Heat capacity can be expressed in many ways; these two posts have chosen per unit mass, perhaps to show that PADI is wrong. But PADI has used the heat capacities per unit volume, which is where they get their "thousands of time greater" from.

Sorry , but words have a precise meaning. Heat capacity is an extensive property, and as such refers to the whole mass of a body, not just to 1 kg. However, as for any extensive quantity, a specific heat capacity is defined, referring ALWAYS and ONLY to the unit mass.
Then there is the volumetric heat capacity, which is defined per unit volume. But if you omit "volumetric", in no way this can refer to the unit volume. Here the good, old Wikipedia:
Heat capacity - Wikipedia
Volumetric heat capacity - Wikipedia
And in any case, there is no direct cause-effect relationship between heat capacity (or volumetric heat capacity) and thermal conductivity.
In a certain sense, they work "one against the other", as the thermal diffusivity is given by the ratio between thermal conductivity and volumetric heat capacity...
Thermal diffusivity - Wikipedia
which explains that thermal diffusivity is the measure of thermal inertia. In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'.
And thermal diffusivity of water is SMALLER than air...

 

[Pedro Burrito]

Spoiler: Answer

c. 20

 

[Joneill]

I did a similar calculation to that of @saxman242 typing while he was posting:

The thermal conductivity of water is 0.6 and that of air is 0.025 W/(m·K), 24 times greater. The PADI Encyclopedia of Recreational Diving says 20 times. We'll have to wait until PB lets us know which answer is "correct", I think I know how this will turn out

Yup - I had slightly different ref #’s so got 23 - but this time the question is definitely flawed as heat capacity and thermal conductivity are 2 different things!

a good reference is here:

Thermal Conductivity of selected Materials and Gases

 

[BlueTrin]

Spoiler: Answer

c. 20

There’s gonna be quite a few people disappointed now

I am one of them

 

[rhwestfall]

NOAA (and I) said 24...

Section 3: Diving Physiology

However, I will not cry about it for the next 24 pages...

 

[saxman242]

Technically PADI is correct here if we're using dry air at 75C...

I'm sure that's what they meant.

 

[scubadada]

OK, PADI answer and real answer, as I thought. They teach it, the test it We all learned, or relearned something from this question.

 

[tursiops]

Sorry , but words have a precise meaning. Heat capacity is an extensive property, and as such refers to the whole mass of a body, not just to 1 kg. However, as for any extensive quantity, a specific heat capacity is defined, referring ALWAYS and ONLY to the unit mass.
Then there is the volumetric heat capacity, which is defined per unit volume. But if you omit "volumetric", in no way this can refer to the unit volume. Here the good, old Wikipedia:
Heat capacity - Wikipedia
Volumetric heat capacity - Wikipedia
And in any case, there is no direct cause-effect relationship between heat capacity (or volumetric heat capacity) and thermal conductivity.
In a certain sense, they work "one against the other", as the thermal diffusivity is given by the ratio between thermal conductivity and volumetric heat capacity...
Thermal diffusivity - Wikipedia
which explains that thermal diffusivity is the measure of thermal inertia. In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'.
And thermal diffusivity of water is SMALLER than air...

Thank you for reinforcing my point. You are choosing your definitions to match your positions.