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Bath vs Cup

In my study of energy, i keep hearing how a bath and a cup or hot water somehow have exactly the same amount of energy, despite the difference in the volume of water. I'd love for one of you geniuses to clarify this, the statement just confuses me.

Reply 1

Stonebridge

Original post by Dottyracer

The statement " a cup of hot water has exactly the same amount of energy as a bath of hot water" is meaningless in physics without further information.

Reply 2

lerjj

Original post by Dottyracer

Presumably the cup of water is hotter?

However, I doubt you can get a 250ml cup of water hot enough to contain the same energy as a 60l bath, with both of them in the same state (liquid presumably...)

CBA to do the calculation but it should be fairly easy to check.

EDIT: this of course assumes we're only discussing thermal energy, otherwise just work out the difference and throw the cu of water at the face of the guy setting the question really fast. (Again, the calc ought to be fairly easy but it's the holidays so.)

(edited 9 years ago)

Reply 3

silentshadows

Your question doesn't make much sense as it stands, so I'm going to make some assumptions.

Heat is a measure of energy. It is measured in joules.

Temperature can be defined as the measure of the vibration of particles (if I remember correctly, there are various other ways to define it as well.)

A cup of water at a high temperature (if I'm remembering correctly, temperature can be defined as the measure of the vibration of particles in a substance) can have the same heat as a bath of water as a lower temperature.

You can use the equation Q=mc∆T to work out changes in thermal energy. Q is thermal energy (heat) and ∆T is the temperature change.

(edited 9 years ago)

Reply 4

Desk-Lamp

The thermal energy is just the kinetic energy of all the particles added together, so it only really depends on the amount of particles, their mass and their average speed (i.e. temperature).

I suppose the point made is that the bath has loads of particles moving really slowly and the cup has a few particles moving really quickly, giving the same energy overall.

I don't know how feasible it is without doing some maths, you might have to freeze the bathwater or something if you have a really small cup :smile: