The First Law of thermodynamics

What is the First Law of Thermodynamics

Conservation of energy, the first law of thermodynamics simple states the the internal thermal energy of a system will not change unless;

1.  Energy is transfered into the system from an object that has a higher temperature.

2. Energy is removed from system because the system does work (like move a piston)

Isobaric Process

An isobaric process is a thermodynamic process in which the pressure remains constant. This is usually obtained by allowed the volume to expand or contract in such a way to neutralize any pressure changes that would be caused by heat transfer.

In an isobaric process, there are typically internal energy changes, work is done by the system, and heat is transferred, so none of the quantities in the first law of thermodynamics readily reduce to zero. However, the work at a constant pressure can be fairly easily calculated with the equation:

W = work done by the system

P = Pressure

V = Volume

U = Internal Thermal Energy

Isochoric Process

An isochoric process is a thermodynamic process in which the volume remains constant. Since the volume is constant, the system does no work and W = 0.

This is perhaps the easiest of the thermodynamic variables to control, since it can be obtained by placing the system in a sealed container which neither expands nor contracts.

Applying the first law of thermodynamics to this situation, we find that:

U = Internal Termal Energy

Q = Heat

Isothermal Process

An isothermal process is a thermodynamic process in which the temperature of the system remains constant. The heat transfer into or out of the system typically must happen at such a slow rate that the thermal equilibrium is maintained.

Other Factors in an Isothermal Process

In general, during an isothermal process there is a change in internal energy, heat energy, andwork.

The internal energy of an ideal gas, however, depends solely on the temperature, so the change in internal energy during an isothermal process for an ideal gas is also 0.

It turns out (and we will explore it more in kinetic gas therory) that the temperature of the gas is directly related to the amount of thermal energy the gas has.

W = work done by the system

U = Internal Thermal Energy

Q = Heat

So if the temperature stays the same, so does the thermal energy.  So when a cylinder expands (or contracts) in an isothermal process the amount heat dumped into (or out of) the gas is equal to how much the work the gas does.

Pressure verses Volume

A to B is an example of a isochoric process, the volume remains constant, but the pressure is increasing.

B to C is an example of a isobaric process, the volume is increased but the pressure is constant.

So an example of what this would look like, consider this.  A cylinder chamber has a one end that can be moved up or down (a piston), this movable end is the Dark gray end, that way the volume of the cylinder can change change.  This movable end can also be locked at any position to maintain a constant volume.  This means we "create" and isochoric process by locking the movable end and removing, or adding heat (thermal energy). A weight is placed on the moving end so we can use this piston to move it up and down.

If we want to move the weight up.

1. The piston is locked into place (so it is a constant volume). On the diagram we're at point A

2. Heat (thermal energy) is applied to the chamber.  At this point the temperature increases and so does the pressure (because we are not talking about the ideal gas law we dont care about the temperature change).  This step is moves us from point A to point B.

3. This piston is released in a way that the pressure in the chamber is constant (so it is a Isobaric process). The constant pressure pushes the piston up lifting the weight upwards.  This is moving from B to C. What's happen is the gases in the cylinder are doing work on the weight (giving it more potential energy), but the energy needed to do that work is coming from somewhere.  Well it comes from the thermal energy of the gas, lowering the temperature of the gas. In an ideal system the amount of work done by the gas is equal to the amount of thermal energy the gas gives up.  The piston is then locked into place, and the pressure is reduced; Step C to D by pulling more thermal energy out.

4. The piston then is pushed downed by the weight.  The work is done in a way to keep the pressure constant. Once again it's a Isobaric process, but unlike the step three were the gas in the cylinder does work to move the piston, in the process the pistons does work on the gas as the cylinder is compressed; step D to A.

Work only happens when the volume changes. If the volume is increased then gas is doing work (think of it, the gas is pushing out cylinder therefore it's doing positive work).  On the pressure verses volume, this when piston moves from B to C

Work only happens when the volume changes. If the volume is decreased then the cylinder is doing work on the gas.  On the pressure verses volume, this when piston moves from D to A

The total work done for the entire cycle is the work done by the gas (From B to C) minus the work done on the gas (From D to A).

Important Equations

For all processes

U = Internal Thermal Energy

Q = Heat input (energy brought into the system)

W = Work output (work done by the system)