AP Physics C questions on the First Law of Thermodynamics with solutions

📚 Quick Study Guide

• 🔥 The First Law of Thermodynamics: This law states that the change in internal energy ($\Delta U$) of a system is equal to the heat added to the system ($Q$) minus the work done by the system ($W$). Mathematically, $\Delta U = Q - W$.
• 🌡️ Internal Energy ($U$): Internal energy is the sum of the kinetic and potential energies of all the molecules in a system. For an ideal gas, internal energy depends only on temperature.
• ⚙️ Work ($W$): Work done *by* the system is considered positive, while work done *on* the system is negative. For a gas expanding or contracting at constant pressure $P$, the work done is $W = P\Delta V$, where $\Delta V$ is the change in volume.
• ☀️ Heat ($Q$): Heat added *to* the system is positive, while heat removed *from* the system is negative.
• 🔄 Thermodynamic Processes:
  • Isothermal: Constant temperature ($\Delta T = 0$).
  • Adiabatic: No heat exchange ($Q = 0$).
  • Isobaric: Constant pressure ($\Delta P = 0$).
  • Isochoric (Isovolumetric): Constant volume ($\Delta V = 0$).
• 📝 Important Note: The first law is essentially a statement of conservation of energy.

Practice Quiz

1. Which of the following statements best describes the First Law of Thermodynamics?
   1. The total energy of an isolated system is constant.
   2. Heat always flows from hot to cold.
   3. The entropy of an isolated system always increases.
   4. Energy can neither be created nor destroyed.
2. A gas expands from a volume of 1.0 m³ to 3.0 m³ at a constant pressure of 2.0 x 10⁵ Pa. What is the work done by the gas?
   1. 2.0 x 10⁵ J
   2. 4.0 x 10⁵ J
   3. 6.0 x 10⁵ J
   4. 8.0 x 10⁵ J
3. In an adiabatic process, which of the following is true?
   1. $\Delta U = 0$
   2. $Q = 0$
   3. $W = 0$
   4. $\Delta T = 0$
4. If 500 J of heat is added to a system and the system does 300 J of work, what is the change in internal energy of the system?
   1. 200 J
   2. 300 J
   3. 500 J
   4. 800 J
5. For an ideal gas undergoing an isothermal process, what quantity remains constant?
   1. Pressure
   2. Volume
   3. Temperature
   4. Internal Energy
6. A rigid container holds a gas. If 200 J of heat is added to the gas, what is the work done by the gas?
   1. 200 J
   2. -200 J
   3. 0 J
   4. 400 J
7. Which thermodynamic process occurs at constant pressure?
   1. Isothermal
   2. Adiabatic
   3. Isobaric
   4. Isochoric