What is the equation of state for isothermal process? Plot P versus V graph and P versus T graph for isothermal process for an ideal gas. Discuss the isothermal process using first law of thermodynamics.
An ideal gas equation is, PV = nRT Since in isothermal process, T is constant, therefore the equation of state for isothermal process reduces to PV = constant P versus V graph and P versus T graph for isothermal process is as shown below.
Derive an expression for the work done by a gas undergoing expansion from volume V1 to V2.
Let us consider an ideal gas enclosed in a cylinder fitted with massless and frictionless piston. Let A be the area of cross-section of piston. Let V be the volume and P be the pressure exerted by gas on the piston. The piston is kept in equilibrium by applying pressure P from outside.
Let the applied pressure be decreased by infinitesimally small amount, so that the piston moves by infinitesimal distance dx. The amount of work done by the gas in infinitesimal expansion is,
where dV = Adx, the infinitesimal increase in volume. Total work done by gas in expanding it from volume V1 to V2 can be obtained by integrating equation (1) from V1 to V2 i.e.