Why is heat measured in joules?

[stevendaryl]

So during the slow compress the gas keeps gaining and losing heat to the surrounding medium at the same rate staying at an equilibrium position with surrounding, so its temperature stays constant

Normally, compressing a gas would cause it to get hotter. But you can view isothermal compression as a limiting case of the following process:

Compress the gas a tiny bit.
Let it cool off.
Compress it a tiny bit more.
Let it cool off.
Etc.

The resulting pressure when you reach your final volume will be less than it would have been if you hadn't allowed it to cool off.

Isothermal compression results in this relationship between pressure and volume:

$P \propto V^{-1}$

If the gas were prevented from exchanging heat with the reservoir, the relationship would be:

$P \propto V^{-5/3}$ (for a monatomic gas).

 

[sophiecentaur]

So during the slow compress the gas keeps gaining and losing heat to the surrounding medium at the same rate staying at an equilibrium position with surrounding, so its temperature stays constant

If you change the volume 'slowly enough' the temperature can remain 'near enough' constant. It's an ideal scenario. The other extreme case - adiabatic volume change, assumes that no heat enters of leaves but that again is only an ideal situation. Real life is always somewhere in between.

 

[Entanglement]

If you change the volume 'slowly enough' the temperature can remain 'near enough' constant. .

If it's not done slowly it will gain heat, but eventually it will lose it reaching to an equilibrium state with the surrounding medium, so the final result is the same whether it's done slowly or fast, why should be so careful about that point ??

 

[WannabeNewton]

The microscopic kinetic energy of the molecules does not correspond to temperature. The quantity that corresponds to temperature is $\frac{\partial{E}}{\partial{S}}$ where $S$ is the entropy...

For a classical gas the equipartition theorem states that the kinetic energy of each mole of the gas is directly proportional to the temperature of the gas. The definition $T = \frac{\partial \bar{E}}{\partial S}$, or even better $S = -\frac{\partial F}{\partial T}$ in the Helmholtz representation, does not contradict this as the equipartition theorem is proven using the statistical equivalent of that latter definition i.e. $\bar{E} = -\frac{\partial}{\partial \beta}\ln Z$. Sure the kinetic energy is itself not temperature but for classical gases it is directly proportional to it as are the energies of other quadratic degrees of freedom.

To the OP: heat $\delta Q$ measures the extent to which the change $\Delta U$ in the internal energy of a system through a process fails to be adiathermal. As others have noted, one can perform simple experiments to show that a quantity $\delta Q$ must exist to account for the change in internal energy of a system between equilibrium states that is not already taken into account by the work done on the system during the process and we know such a quantity must exist simply due to the existence of processes which are the entire opposite of adiabatic and which involve no work done at all but still have a change in internal energy (just take a beaker of water and put a lit Bunsen-burner under it). Clearly then $\delta Q$ must be measured in Joules.

 

[stevendaryl]

If it's not done slowly it will gain heat, but eventually it will lose it reaching to an equilibrium state with the surrounding medium, so the final result is the same whether it's done slowly or fast, why should be so careful about that point ??

Well, if the temperature is (approximately) constant, then the process is (approximately) isothermal. It's just a matter of definition.

You're right that for an ideal gas, the final state doesn't depend on whether the process was isothermal, or not. But the total work done and the change in the entropy of whatever system was compressing the gas depends on whether it was isothermal or not.

 

[Jobrag]

During his honeymoon in Switzerland Joule along with Thompson, (history does not relate why Joules and Thompson happened to meet in Switzerland during Joule's honeymoon), attempted to measure the temperature difference between the top and bottom of a waterfall, history also fails to mention what Joule's bride Amellia thought of it.

 

[stevendaryl]

During his honeymoon in Switzerland Joule along with Thompson, (history does not relate why Joules and Thompson happened to meet in Switzerland during Joule's honeymoon), attempted to measure the temperature difference between the top and bottom of a waterfall, history also fails to mention what Joule's bride Amellia thought of it.

That's funny. Maybe the story was twisted for the sake of New Yorkers like me, but I thought t was Niagara Falls.

 

[Entanglement]

Well, if the temperature is (approximately) constant, then the process is (approximately) isothermal. It's just a matter of definition.
You're right that for an ideal gas, the final state doesn't depend on whether the process was isothermal, or not. But the total work done and the change in the entropy of whatever system was compressing the gas depends on whether it was isothermal or not.

In case of the isothermal process, If the walls of the container are movable, and then the gas is compressed, part of the energy will be used up to expand the volume and the other part will increase the gas's temperature which will eventually get lost to the surrounding reaching a state of thermal equilibrium ( the temperature won't change ) ?

 

[stevendaryl]

In case of the isothermal process, If the walls of the container are movable, and then the gas is compressed, part of the energy will be used up to expand the volume and the other part will increase the gas's temperature which will eventually get lost to the surrounding reaching a state of thermal equilibrium ( the temperature won't change ) ?

If it's isothermal, then none of the energy goes into raising the temperature of the gas.

Some of the energy required to compress it will go towards decreasing the volume, and some of the energy will go towards heating up the reservoir (by assumption, the reservoir is so large that this extra heat causes no significant change to the temperature of the reservoir.

 

[sophiecentaur]

That's funny. Maybe the story was twisted for the sake of New Yorkers like me, but I thought t was Niagara Falls.

Switzerland, almost certainly. I'm not sure Niagra is high enough, in any case. I seem to remember doing the sums and we're talking in terms of something like 0.1C, iirc.

I seem to remember another story about Joule who took enough food with him to provide himself with enough energy to climb a mountain (just enough to achieve the 'work done'). He forgot about the food needed just to keep warm and got back in a bit of a state. Hard to believe an experienced experimenter would make such a trivial mistake - but, brain the size of a planet, and all that.