The First Law of Thermodynamics

From the previous post we learned that energy can be transferred back and forth between the system and the surroundings in both open system and closed system in the forms of work and heat.  Meaning energy can be transformed from one form to another, and it can be transferred from the system to the surroundings or vice versa.  This universal truth is known as the First Law of Thermodynamics, and can be summarized by the simple statement, Energy is conserved.  Energy cannot be created nor destroyed it can be converted from one form to another.  The energy that is lost in the system is gained by the surroundings and vice versa.

Internal Energy

Internal energy of the system is the sum of the kinetic energy and potential energy of all the components of the system.  Kinetic energy components consists of various types of molecular motion and the movement of electrons within molecules.  Potential energy is determined by the attractive interactions between electrons and nuclei and repulsive interaction between electrons and between nuclei in the individual molecule as well as the interaction between molecules. Internal energy here is symbolize as E, and ∆E for change in internal energy.  To calculate the change in internal energy,

∆E = E_final - E_initial

Thermodynamics quantities such as ∆E have three parts: a number and a unit that together give the magnitude and unit of the change, and a sign that give the direction.  A positive value of ∆E results when the E_final.> E _initial, which means that the system has gained energy from the surroundings.  A negative value of ∆E results when E_final <  E_initial, which means the system lost heat to its surroundings.

Relationship between ∆E to Heat and Work

In chemistry, we are concerned with the energy changes occurring in the system and not the surroundings.  Therefore the more useful form of equation of the First Law of Thermodynamics is

∆E = q  + w

        where ∆E is the change in the internal energy
                    q is the head added or liberated from the system
                    w is the work done on or by the system

The equation above says that the change in the internal energy of the system, ∆E is the sum of the heat exchange, q,  between the system and the surroundings and the work done, w, on (or by) the system.  For the sign convention for q and w are as follows:

     - q is positive for an endothermic process and negative for exothermic process
     - w is positive for the work done on the system by the surroundings and negative for work done by the system to the surroundings

Sign Convention Used  and the Relationship among q, w, and ∆E

Sign Convention for q:
q > 0 :  Heat is transferred  from the surroundings to the system

q < 0 :  Heat is transferred  from the system to the surroundings

Sign Convention for w:
 w > 0 :  Work is done by the surroundings on the system

w < 0 :  Work is done by the system on the surroundings


Sign of ∆E = q +  w
q > 0 and w > 0 :  ∆E > 0

q < 0 and w < 0 :  ∆E < 0

q > 0 and w < 0 : The sign of ∆E depends on the magnitude of q and w

q < 0 and w > 0 : The sign of ∆E depends on the magnitude of q and w


Sample Problem:
The hydrogen and oxygen in the cylinder are ignited.  As the reaction occurs, the system loses 1150 J of heat to the surroundings.  The reaction also causes the piston to rise as the hot gases expand.  The expanding gas does 480 J of work on the surroundings as it pushes against the atmosphere.  What is the change of the internal energy of the system?

Solution:

∆E = q  +  w
     = (-1150 J) + (-480 J) = -1630 J

 Both heat and work have negative sign based from the convention sign above.  This means that the system transferred 1630 J of energy to the surroundings.


Try This:
Calculate the change in the internal energy of the system for for a process in which the system absorbs  140 J of heat from the surroundings and does 85 J of work on the surroundings.

Endothermic and Exothermic Processes

Endothermic occurs when a process occurs in which the system absorbs heat.  During this process, heat flows from the surroundings to the system, such as the melting of ice.  Ice absorbs the heat from the surrounding that is why it melts.

Exothermic occurs when the system evolves heat to the surroundings.  During this process, heat flows out of the system into the surroundings,  such as the dissolution of NaOH in water.  As the NaOH pellets dissolve in water it evolves heat to the surrounding water.

State Function

State Function is the property of the system that is determined by specifying its condition or its state (in terms in temperature, pressure, location, and so forth).  The value of a state function depends only on its present conditions not on the particular history of the sample.  Because E is a state function, ∆E depends only on the initial and final states of the system, not on how the change occurs. 

Although ∆E is a state function, q and w are not.  The specific amount of heat and work produced during a change in the state of the system depend on the way in which the change is carried out.