# Ideal Gas

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 $$PV=nRT$$where $n$ is the number of moles of gas, and $R=8.314\ \mathrm{J\ mol^{-1}\ K^{-1}}$ is the gas constant.

show/hide
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.

$$P_iV_i^\gamma=P_fV_f^\gamma$$

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.