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LECTURE 3

Page history last edited by msins@gmu.edu 10 years, 4 months ago

 

LECTURE 3

 

Dr Cooper's comments:

 

 

Jackie Ta (Red)

 

Internal Energy:

     Internal energy is defined as the total energy – kinetic and potential energy – of a system. Kinetic energy is basically a result of motion of molecules present in the system; and potential energy is not associated with that due to its location and gravity or electric field.

     Generally, internal energy cannot be measured; however, change in internal energy, called ∆U, can be calculated (in Joule) using the following equation:

     Equation 1:

Intensive vs. Extensive Property:

  •      Intensive property: depends on the amount of substance in a sample

                    Example: mass (the more substance is added, the higher the mass)

  •      Extensive property: does not depend the amount of substance in a sample

                    Example: gravity (regardless of how heavy two objects are, they both have the same gravitational acceleration)

Properties of Internal Energy:

  •      It is a state function: meaning that the value U depends solely on the beginning and ending state of the system, regardless of how it reaches its final state.
  •      It is an extensive property: more gas added to a system results in change of its internal energy.

 

First Law of Thermodynamics:

     The law states that the change in internal energy of a system equals the sum of the change in heat being added to or lost from and the change in work done on or by the system.

 

     Equation 2:

     

          q: heat flow into (q>0) or out (q<0) of the system. 

          w: work done on (w>0) or by (w<0) the system. 

     

     Note: 

     Sign convention assigns negative value to action that results in the loss of energy, such as in the case of heat flow out of the system or work is done to surroundings by the system; and vice versa.

     In an isolated system where there is no energy exchange, internal energy of that system remains constant.

     Therefore, if work is being done on the system by surrounding, the amount of energy gained will evolve as heat to the environment.

 

Expansion Work:

     Expansion work is a result of volume change such as work done by gas in a container as it expands and raises a piston against its surrounding atmosphere. It is measured as the following:

     Equation 3: 

 

 



          F: force from the surrounding acting on piston 

          A: surface area of piston

          pex: external pressure from atmosphere 

          dz: change in displacement of piston 

          dV: change in volume during expansion 

   

     As gas expands from initial volume, Vi, to final volume, Vf, the work is done by system is measured as in Equation 4. By evaluating the integral, numerical value of work is obtained, which is simply the negative of the product of external pressure and change in volume.

     Unit of work is Joules (J). But work in chemistry is typically expressed in kJ/mol for comparison purpose.

 

     Equation 4:

 

      Note: 

     Negative sign indicates the loss of energy as the system expands and does work on the environment. If calculated result is less than 0, the system has undergone expansion and therefore, lost energy, whereas positive result means it has been compressed by the environment and gained energy.

 

 

 

Michael Sins (blue) 

Free Expansion

Just as the name implies, free expansion is the expansion of a gas that is free. There is no work done by the gas as it expands or enters into a space. This can only take place when the opposing force equals zero such as in a vacuum.  Free expansion incorporates the equation w = 0 (with w representing work), this is due to there being no opposing force. There must be some kind of counter acting force to do work.

Unlike real gases, an ideal gas will not experience a change in temperature because there is no work being done.

 

Expansion against constant pressure

The surroundings of a system will determine whether or not pressure is constant. Having constant pressure can take place when the atmosphere is what surrounds the system. Atmospheric pressure varies only slightly daily so it can be considered constant. If pressure is constant during the expansion of a gas, it will eventually reach equilibrium. With contant pressure being outside the integral for the equation for total work, we can deduce that: 

 eq=w=-Pex \int_{V_i}^{V_f} dV=-Pex(V_f-V_i)

With this equation all we need now is to insert the change in volume which is,

 

eq=\Delta V=V_f - V_i

 

Knowing this we can simplify the recently stated equation for work and rewrite it as

 

 
eq=w=-Pex \Delta V 

 

Here our constant external pressure is multiplied by our change in volume to obtain a value for work.

 

In order to gain a better grasp on the idea of a gas doing work by expanding against a constant pressure refer to the depiction below, known as an indicator diagram. Here we can clearly see how an integral can be represtented by Area, with area being equal to external pressure multiplied by the change in volume.

 

 

Reversible Expansion

 

A system is in equilibrium when changes in its surrounding result in an equal but opposite change in the system, these changes are referred to as being infinitesimal. In a reversible process the system is in total equilibrium at every stage with its surroundings. This will allow any change in progress to be halted and reversed when ever necessary. The idea of infinitesimal modifications on variables in order to maintain control of the system is the base of a reversible expansion. Temperature can bring to mind a clear veiw of this process, if a system is at equilibrium with its surroundings and the system's temperature is lowered, energy will flow from the surroudings of that system into the system itself. The exchange will reverse the system back to its original temperature thus maintaining an equilibrium.

 

 

 

Isothermal Reversible Expansion:

Razia Sultana (black)

An Isothermal Reversible Expansion process is a thermodynamics process in which the temperature of the system stays constant.  This typically occurs, when the expansion is made isothermal by keeping the system in thermal contact with its surroundings.  As a result, we can use ideal gas law which is pV=nRT to know the pressure of each stage of the expansion.  However, since temperature is constant in an isothermal expansion, we may take out the n and R outside the integral, therefore our equation is:

 

Formula

 

The above equation states that: 

 

When the final volume is greater than the initial volume, as in an expansion, the logarithm in equation above is positive and thus W < 0, which mean the system has done work on the surroundings by pushing the surrounding air upwards.  The equation also states that, the higher the temperature is the more work is done.  We can also include that more work is obtained when the expansion is reversible because matching external pressure to the internal pressure at each stage of the process ensures that none of the system’s pushing power is wasted.  Moreover, the maximum work is obtained in the system when changes take place reversibly as the equation at the bottom  demonstrate it:

 

Formula 

 

An example of the main above equation to see if it applies to all substances and to all kinds of work:

 

Calculating the work of gas production:

 

*Calculate the work done when 50g of iron reacts with hydrochloric acid in (a) a closed vessel of fixed volume, (b) an open beaker at 25˚C.

 

-In (a) the volume cannot change, so no expansion work is done, therefore W=0.

-In (b) the gas drives back the atmosphere and therefore we can neglect the initial volume because the final volume is much larger. As a result:

 

W=–PexΔV                     (ΔV=final volume of gas)

V= nRT/Pex               

W= –Pex × nRT/Pex= –nRT

M (H2) =n (Fe) =50g/55.85g mol‾1

Therefore:

W= –PexΔV ≈ –Pex × nRT/Pex =–nRT

 

W=-50g/55.85g mol × (8.3145 J K mol) × (298 K)

≈–2.2 KJ

 

-So the system does 2.2 KJ of work driving back the atmosphere. And equation worked perfectly for this perfect gas system.

 

 

Varieties of work:

 

 

Type of work                                Dw                                   Comments

 

 

Volume Expansion                    w = - ò Pext dV                    (P = pressure) 

 

Stretching                                  w = - ò g dl                           (g =tension)

 

Surface Expansion                     w = - ò g d s                        (g = surface tension)

 

Electrical                                    w =  ò f dq                           (f = electrical potential)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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