Ideal Gas

Tasks

  1. Compress air in a syringe isothermally (at constant temperature) and predict its final pressure.
  2. Compress the air in the syringe adiabatically and measure the ratio of specific heats (\gamma) for air.
  3. 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.

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An isothermal process is one in which the temperature of a quantity of gas is held constant while the volume and pressure change, in which case
\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)}

where the quantity \gamma is called the ratio of specific heats and depends on the gas. For air, the value is approximately 1.4.