The gas is compressed slowly to show how heat transfer and the type of gas affect its temperature change.
Adjust conditions:
The sliders adjust the values
体積を半分にすると絶対温度は何倍か？
同じ初期状態から同じ体積まで圧縮する。温度一定なら必要な仕事は断熱と比べて？
The equations explain the phenomenon
1The molecules' kinetic energies are added togetherU=N · ½ m ⟨v²⟩=(32) n R T……
2The molecule's speed perpendicular to the piston after a collision is determinedvx′=vx+2u……
3The increase in kinetic energy in a single collision is calculatedΔE≒2 m vx · u……
4The energy increases from all collisions are added togetherdU=p S u dt=−p dV……
5The energy balance includes heat transferΔU=Q+W……
6Small changes in temperature and volume during adiabatic compression are relateddTT=−(2/3) dVV……
7Integration gives the temperature ratioT₂T₁=(V₁V₂)2/3……
8Approximate simulation of molecular motionMolecular calculation:T₂T₁≒1.598 (adiabatic)，1.01 (constant temperature)……
Further topics: compression at constant temperature, pressure, and specific heat capacity
9The gas is compressed at constant temperatureW=n R T ln(V₁V₂)=−Q……
10The result is expressed as a relationship between pressure and volumep V5/3=Constant……
11The gas is heated at constant volumeQ=(32) n R ΔT……
12The gas is heated at constant pressureCp=CV+R……
What this chapter has shown
A molecule that strikes an approaching piston rebounds at a higher speed. If no heat is transferred, the internal energy increases by the amount of work the piston does on the gas. The temperature therefore rises even without heat being added.
A factor of 1.59Temperature ratio for adiabatic compression of a monatomic gas
Compression at constant temperature from the same initial state to the same final volume releases heat equal to the 69 J of work done on the gas.
In everyday lifeA diesel engine compresses air to a high temperature to ignite the fuel.
Detailed summary
A gas heats up when compressed because molecules that collide with the approaching piston rebound at higher speeds. Adding up the increases in kinetic energy for all the molecules gives −p dV, the small amount of work done by the piston. Including the heat Q transferred through the walls gives the first law of thermodynamics, ΔU = Q + W. This law applies the conservation of energy derived from the equations of motion to a large collection of molecules. If no heat escapes, halving the volume increases the temperature by a factor of 22/3.