# Does a thermometer drifting down a river measure a different temperature than a still thermometer?

Let's say I took a thermometer and affixed it to the end of a poll. Then I went halfway across a bridge and held the other end of the poll and dipped the thermometer into the middle of a river and just held it there. Then I sent my friend upstream a bit and he walked halfway across a bridge up there and dropped one of those floating thermometers into the river and let it float / drift down the middle of the river toward me.

When the floating thermometer came drifting by me where I had the fixed thermometer I could see both thermometers at the same time. Would they both measure the same water temperature?

(Please allow me to say that the resin that affixed the thermometer to the poll was a perfect insulator. I.e. the thermometer was measuring the water temperature and none of the poll temperature.)

• See my comment to Niels's answer: Is this a question about whether the translational kinetic energy counts in the measurement of heat? – Selene Routley Jan 23 '18 at 4:28
• Depending on the intended meaning of the question physics.stackexchange.com/questions/96327/… may be a duplicate. – dmckee --- ex-moderator kitten Jan 23 '18 at 4:28
• Assuming that thermometer responds to temperature changes quickly enough, both thermometers, moving and stationary, must measure (nearly) the same temperature (in the neighbourhood) of a point at the same time. – Deep Jan 23 '18 at 4:32
• It really depends on the meaning of the Q.... – Alchimista Jan 23 '18 at 13:27
• Yes the my question is, would the translational kinetic energy be measured as heat causing a higher temperature measured by the still thermometer. – Joe C Jan 25 '18 at 0:15

## 3 Answers

a thermometer which drifts with the current (at the same speed) will be stuck measuring the temperature of the same body of fluid surrounding it. the expectation in this case is that its reading will change only very slowly over time. On the other hand, the thermometer which is fixed in position and not drifting with the flow will be sampling a different body of water at each instant of its operation, and will capture changes in the temperature of the flow which the drifting thermometer cannot.

• I think the OP probably is thinking of the case where the river water is all at perfectly uniform temperature. I'm guessing this is a question about whether the translational kinetic energy is counted in the heat content – Selene Routley Jan 23 '18 at 4:26
• It might help to use extremes. What would you expect if the water was flowing, let’s say, 80 mph. Would the friction affect the stationary thermometer? – Lambda Jan 23 '18 at 4:44
• probably not, but experiments are possible! – niels nielsen Jan 23 '18 at 7:06
• I meant if the entire river were the same temperature. – Joe C Jan 25 '18 at 0:16
• if it were, there probably would be no signal. – niels nielsen Jan 25 '18 at 0:52

Temperature is a thermodynamic variable but temperature is also defined with statistical methods on the molecules, in your question water.

Where the velocity is the random velocity of molecules in the fluid. If you take a cup of water at a temperature T and put it on a moving train, the temperature derived statistically will not change .

Higher order effects may make a small difference. For example, the water under the bridge will have higher temperature than the water up river because of the change of potential energy to kinetic energy of the water , whereas the trapped floating box only by conduction will acquire more average molecular kinetic energy.

Perhaps friction might be at play. The thermometer which moves with the river experiences less friction than that at a fixed position, constantly hit by oncoming water, while the other goes with the flow. Hence, it may be likely that the stationary thermometer may produce a higher reading over time due to the friction it experiences with the water gushing by.