Ideal Gas
Tasks
- Compress air in a syringe isothermally (at constant temperature) and predict its final pressure.
- Compress the air in the syringe adiabatically and measure the ratio of specific heats (\gamma) for air.
- Observe an isochoric (constant-volume) process and predict the change in pressure.
Resources
- Plastic syringe with volume markings
- Temperature and pressure sensors, ScienceWorkshop interface
- DataStudio software and idealgas setup file
Background
At normal conditions, such as standard temperature and pressure, most gases behave like an ideal gas. This is a theoretical gas composed of randomly moving, non-interacting point particles. The pressure P, volume V, and temperature T of an ideal gas obeys the relation PV=nRTwhere n is the number of moles of gas, and R=8.314\ \mathrm{J\ mol^{-1}\ K^{-1}} is the gas constant.
show/hide\frac{P_i}{P_f} = \frac{V_f}{V_i}
An isochoric process is one in which the volume remains constant, usually because the gas is in a rigid container. \frac{P_i}{P_f}=\frac{T_i}{T_f}
If the pressure of a gas remains the same while its temperature and volume can change, the process is isobaric. \frac{V_i}{V_f}=\frac{T_i}{T_f}
In the three previous processes, the gas has to exchange heat with its environment in order for the change to occur. If the heat energy of the gas remains constant – for example if it is in an insulated container or the process occurs very quickly – the process is called adiabatic. The pressure, volume, and temperature of a gas will all change during an adiabatic process.
For an adiabatic process:
P_iV_i^\gamma=P_fV_f^\gamma
and thus
\gamma = \frac{\log(P_i/P_f)}{\log(V_f/V_i)}
or alternatively \gamma=\frac{\log(P_i/P_f)}{\log(P_i/P_f)+\log(T_f/T_i)}
where the quantity \gamma is called the ratio of specific heats and depends on the gas. For air, the value is approximately 1.4.