Is a Shower Hotter than a Hot Tub?

• People living in the same house may use the same shower. Each person might have their own preference and set it to a different temperature.
  • Are we referring to one shower "session", or all showers from one specific shower "head"?
• The water in a shower is hotter right as it leaves the shower head. It cools down as it passes through the air before reaching your body.
  • Where are we putting the thermometer?
• In the summer, and especially in hot countries, many people will have cold showers.
  • Some showers aren't hot at all.
• In countries like Finland, people sometimes spend a lot of time in saunas.
  • Sometimes there is a third, related option.
• The water in a hot tub may periodically need to be exchanged with fresh water.
  • Are we only measuring the water that is currently in the hot tub? What about the water that used to be in the hot tub but is now on it's way down the drain and out to sea?
• The water from a shower also goes down the drain.
  • How do we define the beginning and end of a shower both in space and in time? Is it the space between the shower head and the drain? Or is it the single point in space where the water first touches your skin? Is it from the time you first turn on the shower, or from the time you first step into the shower?
• Hot tubs often stay filled with water and are maintained at a certain temperature to prevent the growth of algae.
  • Should we also only measure the temperature of a hot tub while it is being used? Because that's how we measure showers. Measuring a hot tub when it's not being used would be unfair to showers.
• A hot tub holds much more water than the amount of water produced by a shower head during an average shower.
  • A small quantity of hot water does not feel as hot as being submerged in a large quantity of slightly cooler water.
• We can measure the average temperature of a shower over time.
  • Error: NaN. (The shower was off. There was nothing to measure.)
• What if we estimated the average temperatures of all modern day showers within the United States, only when they are running, and while also ignoring the "warm up" period when it was just turned on.
  • Including the showers on cruise ships that are currently docked at US ports?
• Yes. Give me a yes or no answer, is a shower hotter than a hot tub?
  • Is a Jacuzzi a hot tub?
• Yes.
  • Is a Roman bath thousands of years ago a hot tub?
• No.
  • Is an elephant standing under a waterfall having a shower?
• Yes.
  • Is a person caught in the rain having a shower?
• No.
  • The answer is not always yes or no. Sometimes they are the same temperature.
• Fine. What is the temperature of all modern day showers within the United States, only during winter, only measured while they are running, and ignoring the warm up period after it was just turned on?
  • The average temperature for showers is generally between \(98^{\circ }F\) (\(37^{\circ }C\)) and \(105^{\circ }F\) (\(41^{\circ }C\))
• What is the average temperature of all modern day hot tubs within the United States that are filled with water and where someone is either sitting in them or where they are about to sit in them?
  • The average temperature for hot tubs is between \(98^{\circ }F\) (\(37^{\circ }C\)) and \(102^{\circ }F\) (\(39^{\circ }C\))
• Which is hotter?
  • The average shower is probably either the same or slightly hotter than the average hot tub. The 99th percentile of hottest hot showers are probably a bit hotter than the 99th percentile of hottest hot tubs.

(In case you think I have a weird interest in obscure facts about showers and hot tubs, you're correct. However, this is also intended as a metaphor.)