Rüchardt experiment
If a gas is compressed adiabatically, i.e. without outflow of heat from the system, the temperature rises (due to the pressure increase) at a higher rate with respect to isothermal compression, where the performed work is dissipated as heat.
, with which the expansion of the gas can be calculated by the application of heat is called the isentropic – or adiabatic coefficient.
For example, a steam turbine is not isentropic, as friction, choke and shock processes produce entropy.
A typical experiment,[4] consists of a glass tube of volume V, and of cross-section A, which is open on one of its end.
A ball (or sometimes a piston) of mass m with the same cross-section, creating an air-tight seal, is allowed to fall under gravity g. The entrapped gas is first compressed by the weight of the piston, which leads to an increase in temperature.
The picture shows a revised version of the original Rüchardt setup: the sphere oscillating inside the tube is here replaced by a "breast-pump" which acts as an oscillating glass-piston; in this new setup three sensors allow to measure in real-time the piston oscillations as well as the pressure and temperature oscillations of the air inside the bottle (more details may be found in [5]) According to Figure 1, the piston inside the tube is in equilibrium if the pressure P inside the glass bottle is equal to the sum of the atmospheric pressure P0 and the pressure increase due to the piston weight : When the piston moves beyond the equilibrium by a distance dx, the pressure changes by dp.
3 as follows: Solving this equation and rearranging terms yields the differential equation of a harmonic oscillation from which the angular frequency ω can be deduced: From this, the period T of harmonic oscillation performed by the ball is: Measuring the period of oscillation T and the relative pressure P in the tube yields the equation for the adiabatic exponent:
