Let us understand changes in temperature, pressure, and volume together. This is an application of changes in the state of gases and the first law of thermodynamics.
Basic Knowledge
Types of changes in the state of a gas:
① Isothermal change: Constant temperature (ΔU = 0). When a gas expands, it does work on the outside and absorbs the same amount of heat.ΔU = 0 → Q = W'(W' is work done by the gas)
② Constant-volume change (isochoric change): Constant volume. No work is done on the outside (W' = 0).ΔU = Q(All absorbed heat becomes internal energy)
③ Adiabatic change: No heat enters or leaves (Q = 0).ΔU = -W'(Internal energy decreases by the amount of work done by the gas)
④ Constant-pressure change (isobaric change): Constant pressure. Temperature and volume change.
When a gas does work on the outside during these changes:W' = pΔV(p: pressure, ΔV: change in volume)
Isothermal change（T constant: PV=constant. ΔU=0）
Constant-volume change（V constant: Work on the outside is 0. ΔU=Q）
Adiabatic change（Q=0: ΔU = -W'. Expansion → temperature decreases）
Constant-pressure change（p constant: V∝T. W' = pΔV）
W' = pΔV（Work done by a gas in a constant-pressure change）
Boyle's law（Isothermal: PV = constant）
Charles's law（Constant pressure: V/T = constant）
Further Study (Background and Significance)
Boyle–Charles's law, PV/T = constant, integrates isothermal, constant-pressure, and constant-volume changes. When the amount of gas (number of moles n) and the gas constant R are included, the ideal gas equation PV = nRT is obtained; it also appears in high-school chemistry.
During adiabatic expansion (Q=0, volume increases), internal energy decreases and temperature falls. This is the basic principle of cooling. The outlet of a spray can becoming cold is also an example of adiabatic expansion. Conversely, temperature rises during adiabatic compression (a bicycle pump becomes warm).
When a gas changes state on a p-V graph, the area under the graph represents the work done by the gas. It is useful to understand the shapes of isothermal changes (hyperbolas), constant-pressure changes (horizontal lines), constant-volume changes (vertical lines), and adiabatic changes (steep hyperbolas).
- Isothermal: ΔU=0, Q=W'
- Constant volume: W'=0, ΔU=Q
- Adiabatic: Q=0, ΔU=-W'
- Constant pressure: W'=pΔV
- Adiabatic expansion → temperature decreases (principle of cooling)
- Adiabatic compression → temperature increases
- Area on a p-V graph = work done by the gas
Important Notes (Common Confusions)
① Do not confuse “adiabatic (Q=0)” with “isothermal (T = constant).” Temperature changes during an adiabatic change. ② Definitions of W and W': W = work done on the object from outside, W' = work done by the gas. W = -W'. ③ During a constant-volume change, work on the outside W' = 0, but internal energy changes when heat is supplied. ④ Do not confuse the conditions for applying Boyle's law (isothermal: PV=constant) and Charles's law (constant pressure: V/T=constant).
Practice
- In an adiabatic change, a gas did 250 J of work on the outside. Find the change in internal energy.
- In a constant-volume change, 600 J of heat was supplied to a gas. Find the change in internal energy and the work done by the gas.
- Using the first law of thermodynamics, explain why the temperature of a gas decreases during adiabatic expansion.