Isobaric & Isochoric PV Processes
Visualize work as the area underneath a PV curve. Discover why an Isochoric process performs zero work while an Isobaric process expands or compresses.
CONSTANT PRESSURE AND CONSTANT VOLUME
Thermodynamic processes are often categorized by the physical properties they keep constant. An **isobaric** process occurs at a constant pressure (), where the system usually expands or contracts as heat is added or removed. An **isochoric** (or isovolumetric) process occurs at a constant volume (), meaning the system can do no work () and any heat added directly increases the internal energy and temperature.
WORK AND ENERGY RELATIONSHIPS
In an **isobaric** process, the work done is simply . On a PV diagram, this appears as a horizontal line. In an **isochoric** process, because the volume does not change, the area under the curve is zero, and thus no work is performed. Any energy transfer as heat results in a direct change in internal energy: . On a PV diagram, this appears as a vertical line.
HOW TO USE THIS VISUALIZATION
1. **Select Process Type**: Toggle between Isobaric (horizontal) and Isochoric (vertical) paths on the PV diagram. 2. **Observe the Piston**: Watch the gas particles in the cylinder. Notice that the piston moves during isobaric expansion but is locked in place during isochoric heating. 3. **Calculate Work and Heat**: Use the First Law calculator to track how and contribute to the change in internal energy and temperature . **Try This**: Perform an Isochoric heating. Does the pressure increase or decrease? Now perform an Isobaric heating. Why is more heat required to reach the same final temperature compared to the isochoric case?
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 2: Thermodynamics (Topic 2.2)
Learning Objective: ENE-1.D
COMMON MISCONCEPTIONS
- Thinking work is done when pressure changes (work only happens if volume changes).
- Forgetting that is always greater than .
- Confusing the paths on a PV diagram (Isobaric = Horizontal, Isochoric = Vertical).
KEY TAKEAWAYS
- Isobaric: Constant P, .
- Isochoric: Constant V, .
- Area under PV curve is work.
- Heat capacity depends on the path.
- First Law: .
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): How much work is done by an ideal gas during an isochoric process?
Show Answer & Explanation
Answer: 0 J
Explanation: Work is defined as . In an isochoric process, , so no work is performed by or on the gas.
Q2 (CONCEPTUAL): Which process requires more heat to increase the temperature of a gas by 10 K: isobaric or isochoric?
Show Answer & Explanation
Answer: Isobaric
Explanation: In an isobaric process, heat is needed for both increasing internal energy AND doing work of expansion (). In an isochoric process, all heat goes toward internal energy.
Q3 (QUANTITATIVE): A gas at 2 atm pressure is heated isobarically from 1 L to 3 L. Calculate the work done on the gas (in L·atm).
Show Answer & Explanation
Answer: -4 L·atm
Explanation: L·atm.
DEEP DIVE: RELATED CONCEPTS
In thermodynamics, we study how systems exchange energy with their surroundings through heat and wor...
HEAT ENGINES AND THE SECOND LAWA heat engine is a device that converts thermal energy into mechanical work by taking heat from a ho...
WHAT IS BLACKBODY RADIATION?A blackbody is an idealized object that absorbs all electromagnetic radiation that falls on it. When...
