Lecture Notes: First Law of Thermodynamics

Overview

• First Law of Thermodynamics: The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
• Formula: ( \Delta U = Q - W )
  • ( \Delta U ) = change in internal energy
  • ( Q ) = heat added to the system
  • ( W ) = work done by the system

Example Problems

Example 1: Work done on and heat lost from the gas

• Problem: 60 J of work is done on a gas; the gas loses 150 J of heat.
• Calculation:
  • Heat lost: ( Q = -150 ) J (since heat left the gas)
  • Work done on gas: ( W = +60 ) J
  • ( \Delta U = Q + W = -150 + 60 = -90 ) J
• Conclusion: Gas loses 90 J of internal energy; temperature decreases.

Importance of Internal Energy

• Internal energy is proportional to temperature.
• If internal energy decreases, temperature decreases.
• Cannot directly correlate joules to degrees without further specifics of gas.

Example 2: Heat added and work done by the gas

• Problem: Gas starts with 200 J of internal energy; 180 J of heat is added; gas does 70 J of work.
• Calculation:
  • Heat added: ( Q = +180 ) J
  • Work done by gas: ( W = -70 ) J
  • Change in internal energy: ( \Delta U = Q + W = 180 - 70 = 110 ) J
  • Initial internal energy: 200 J
• Final internal energy: ( U_{final} = 200 + 110 = 310 ) J

Example 3: Work done on and internal energy decrease

• Problem: 40 J of work done on a gas; internal energy decreases by 150 J.
• Calculation:
  • Internal energy decrease: ( \Delta U = -150 ) J
  • Work done on gas: ( W = +40 ) J
  • Solving for heat ( Q ):
    • ( \Delta U = Q + W )
    • ( -150 = Q + 40 )
    • ( Q = -150 - 40 = -190 ) J
• Conclusion: 190 J of heat left the system.

Key Takeaways

• Be cautious with positive and negative signs:
  • Heat added to the system is positive.
  • Heat lost by the system is negative.
  • Work done on the system is positive.
  • Work done by the system is negative.
• ( Q ) is heat, ( W ) is work, and ( \Delta U ) is the change in internal energy.
• Change in internal energy indicates the change in temperature, though not directly measurable as degrees without specific gas details.