SUBJECT : Engg. Thermodynamics TITLE: Ideal gases (Upto Vander waals eqn.) Year : 2014 Presentation By: ( ) SHARMA CHETAN K.

Ideal Gases The gases which follow the gas laws (PV = mRT) )at all ranges of pressures and temperatures are considered as “ideal gases”. ‘Real gases’ follow these laws at low pressures or high temperatures or both. This is because the forces of attraction between molecules tend to be very small at reduced pressures and elevated temperatures.

Boyle’s law.

Charle’s law.

Equation of state for a perfect gas

Equation of state for a perfect gas

p-v-T SURFACE OF AN IDEAL GAS The equation of state of an ideal gas is a relationship between the variables pressure (p), volume (V) and temperature (T). On plotting these variables along three mutually perpendiculars axes, we get a surface which represents the equation of state (pv = RT). Such a surface is called p-v-T surface. Each point on this surface represents an equilibrium state and a line on the surface represents a process.

INTERNAL ENERGY AND ENTHALPY OF A PERFECT GAS Joule’s law states that the specific internal energy of a gas depends only onthe temperature of the gas and is independent of both pressure and volume.. I.e. u = f(T).. From definition of enthalpy, h = u + pv Also pv = RT h = u + RT Since u is a function of temperature only, h is a function of temperature, h = f(T)

SPECIFIC HEAT CAPACITIES OF AN IDEAL GAS

REAL GASES It has been observed that when experiments are performed at relatively low pressures and temperatures most of the real gases obey Boyle’s and Charle’s laws quite closely. But the actual behaviour of real gases at elevated pressures and at low temperatures deviates considerably.

The ideal gas equation pv = RT can be derived analytically using the kinetic theory of gases by making the following assumptions : A finite volume of gas contains large number of molecules. The collision of molecules with one another and with the walls of the container are perfectly elastic. The molecules are separated by large distances compared to their own dimensions The molecules do not exert forces on one another except when they collide.

VAN DER WAALS’ EQUATION

Constants of Van der Waals’ Equation

Case study: Example Example:1 The volume of a high altitude chamber is 40 m3. It is put into operation by reducing pressure from 1 bar to 0.4 bar and temperature from 25°C to 5°C. How many kg of air must be removed from the chamber during the process ? Express this mass as a volume measured at 1 bar and 25°C. Take R = 287 J/kg K for air.