# First law of thermodynamics in layman's term

The first law of thermodynamics

$dU=dQ-dW$

could be expanded to

$dU=TdS-PdV$

where

U is internal energy,
T is temperature,
S is entropy,
P is pressure, and
V is volume.

I am trying to understand the terms one by one in plain English.

So:
V is how big the container is,
P is how hard the container is pushing the system,
U is internal energy of system,
T is how willing the system want to give out heat, and
S is how evenly distributed the thermal energy is.

Plus:
$PdV$ is energy (loss) due to the system pushes out the surroundings to make itself a room, and
$TdS$ is energy due to the particles jumping around.

Is there misconception? and

I don't understand why $TdS$ would be a form of energy, why?

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My (imperfect) understanding based on a short visit to Wikipedia is that the first law of thermodynamics is a simple statement of conservation of energy. That is, the change in thermal energy(heat) of a cooler area is equal to the change in heat of the hotter area - work extracted from the system.

This could be combined with the ideal gas laws (lets see how I remember chemistry...) to relate a change in volume pressure or temperature to work extracted from a system. For example, if 1J of thermal energy is added to an area, and it does .1J of work, then .9J will be transferred as heat energy.

The first law is indeed a statement of the principle of conservation of energy. All forms of energy.

So your equations are only part of the story as there are many more forms of energy. Obviously if all our action takes place on a table top we don't need to consider gravitational energy. Similarly if no electric current is flowing we don't need to consider electric enrgy. and so forth.

With regard to the thermodynamic quantities you mention here is a simple non rigorous answer.

Energy as shown by indicator diagrams. These are graphs connection two (a pair) of variables.

It was realised that the area under a pressure - volume (PV) graph represented work or energy.

Clausius introduced Entropy to pair with temperature to be able to draw a similar graph for heat energy. Again the area under the entropy - temperature (TS) graph gives energy.

The hatched areas in the attachment both represent energy of some sort. Similar indicator diagrams can be drawn for other pairs of quantities

Voltage - Charge
Force - Distance
Surface Tension - Area
Magnetic Field - Magnetic Moment

go well

***

The first law is indeed a statement of the principle of conservation of energy. All forms of energy.

So your equations are only part of the story as there are many more forms of energy. Obviously if all our action takes place on a table top we don't need to consider gravitational energy. Similarly if no electric current is flowing we don't need to consider electric enrgy. and so forth.

With regard to the thermodynamic quantities you mention here is a simple non rigorous answer.

Energy as shown by indicator diagrams. These are graphs connection two (a pair) of variables.

It was realised that the area under a pressure - volume (PV) graph represented work or energy.

Clausius introduced Entropy to pair with temperature to be able to draw a similar graph for heat energy. Again the area under the entropy - temperature (TS) graph gives energy.

The hatched areas in the attachment both represent energy of some sort. Similar indicator diagrams can be drawn for other pairs of quantities

Voltage - Charge
Force - Distance
Surface Tension - Area
Magnetic Field - Magnetic Moment

go well

***

I interpret this as: entropy means how much thermal energy is stored per temperature, treating temperature as some kind of energy storing pocket and the value of entropy tells the ratio. That sounds pretty much like heat capacity to me. Are they actually interchangeable (they have the same unit)?

That sounds pretty much like heat capacity to me.
Not sure what you mean by heat capacity. Are you referring to specific heat capacity (often shortened to specific heat) or to enthalpy?

Not sure what you mean by heat capacity. Are you referring to specific heat capacity (often shortened to specific heat) or to enthalpy?
I mean heat capacity of the whole system, which equals specific heat capacity times mass of system. It has the same unit as entropy (J/K)

That sounds pretty much like heat capacity to me. Are they actually interchangeable (they have the same unit)?
OK now we know you mean specific heat, and considering unit mass to make things easy,

The two quantities are not the same.

There are many cases in Physics where two things have ostensibky the same units but are different

eg work and moment both have units of Newton-metres but I'm sure you realise they are very different.

In this case Entropy is the ration of heat (only) exchanged divided by the absolute temperature the exhange takes place at. There is only one temperature.

The heat taken up in heating the mass changes the temperature and the amount of heat = spcific heat times temperature difference.

go well