Download Work in Thermodynamic Processes - General Physics I - Lecture Slides and more Slides Physics in PDF only on Docsity!
Work in Thermodynamic Processes –
State Variables
- State of a system
- Description of the system in terms of state variables
- Pressure
- Volume
- Temperature
- Internal Energy
- A macroscopic state of an isolated system can be specified only if the system is in internal thermal equilibrium
Work
- Work is an important energy transfer
mechanism in thermodynamic
systems
- Heat is another energy transfer
mechanism
- Example: gas cylinder with piston
- The gas is contained in a cylinder with a moveable piston
- The gas occupies a volume V and exerts pressure P on the walls of the cylinder and on the piston
Work on a Gas Cylinder
- When the gas is compressed
- ΔV is negative
- The work done on the gas is positive
- When the gas is allowed to expand
- ΔV is positive
- The work done on the gas is negative
- When the volume remains constant
- No work is done on the gas
W = - P ΔV
Notes about the Work Equation
constant during the
expansion or compression,
the process is called an
isobaric process
- If the pressure changes, the
average pressure may be
used to estimate the work
done
W = - P ΔV
Work done on the gas Work=Area under the curve
W = - P ΔV
PV Diagrams
- The curve on the diagram is called the path taken between
the initial and final states
- The work done depends on the particular path
- Same initial and final states, but different amounts of work are done
Question
Find work done by the gas in this cycle. P 2 P 1 V 1 V 2
Other Processes
- Isovolumetric
- Volume stays constant
- Vertical line on the PV diagram
- Isothermal
- Temperature stays the same
- Adiabatic
- No heat is exchanged with the surroundings
W = nRT ln
Vf
V
i
& =^ PiVi ln^
Vf
V
i
Example:
Given: n = 1 mole Ti = 96.2 K Tf = 144.3 K Vi = 0.2 m^3 Vf = 0.3 m^3 P = const Find: W=? ( ) ( ) J W P V PVf Vi m 400 4000 Pa 0.3m 0. 2 3 3 = = Δ = − = −
- Isobaric expansion: Calculate work done by expanding gas of 1 mole if initial pressure is 4000 Pa, initial volume is 0.2 m 3 , and initial temperature is 96.2 K. Assume a two processes: (1) isobaric expansion to 0.3 m 3 , Tf=144. K (2) isothermal expansion to 0.3 m 3 . Also:
- 5
- 2
- 3 3 3 = = = = m m V V nR P V nR P V T T i f i i f f i f A 50% increase in temperature!
Processes for Transferring Energy
• By doing work
- Requires a macroscopic displacement of the point of
application of a force
• By heat
- Occurs by random molecular collisions
• Results of both
- Change in internal energy of the system
- Generally accompanied by measurable macroscopic
variables
- Pressure
- Temperature
- Volume How can energy be transferred?
First Law of Thermodynamics
• Consider energy conservation in thermal
processes. Must include:
- Q
- Heat
- Positive if energy is transferred to the system
- W
- Work
- Positive if done on the system
- U
- Internal energy
- Positive if the temperature increases
Applications of the First Law:
1. Isolated System
- An isolated system does not interact with its
surroundings
- No energy transfer takes place and no work is done
- Therefore, the internal energy of the isolated system
remains constant
Example:
Given: n = 1 mole Vi = 0.2 m^3 Vf = 0.3 m^3 P = const Q=500 J Find: Δ U=? ( ) ( ) J W P V PVf Vi m 400 4000 Pa 0.3m 0. 2 3 3 = = Δ = − = −
- Isobaric expansion: If 500 J of heat added to ideal gas that is expanding from 0. m 3 to 0.3 m 3 at a constant pressure of 4000 Pa, what is the change in its internal energy? Use 1 st law of thermodynamics: U Q W J J J
Q U W
Example: Cyclic Process in a PV Diagram
- This is an ideal monatomic gas confined in a cylinder by a moveable piston
- A to B is an isovolumetric process which increases the pressure
- B to C is an isothermal expansion and lowers the pressure
- C to A is an isobaric compression
- The gas returns to its original state at point A
Applications of the First Law:
3. Isothermal Processes
- Isothermal means constant
temperature
- The cylinder and gas are in
thermal contact with a large
source of energy
- Allow the energy to transfer into
the gas (by heat)
- The gas expands and pressure
falls to maintain a constant
temperature (ΔU = 0 )
- The work done is the negative
of the heat added
ln. f i ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = V V W nRT
