Isobaric process : this is a thermodynamic process that occurs at constant pressure .even through pressure is constant in this process , temperature , volume and internal energy are not constant . From the ideal gas equation we have
` V= ((mu R )/( P ))T `...(1)
Here `(mu R) /( P) = ` constant
In an isobaric process the temperature is directly proportional to volume .
` V porp T ` ( Isobaric process )
THis implies that for a isobaric process , the V-T graph is a straight line passing through the origin .
IF a gas goes from a state `(V_i , T_i ) ` to` (V_f , T_f)` at constant pressure then the system satisfies the followinng equation
` (T_f )/(V_f )=(T_i )/(V_i)`
Examples for Isobaric process :
( i ) when the gas heated and pushes the piston so that it exerts a force equivalent to atmospheric pressure plus the force due to gravity then this process is isobaric .
(ii ) Most of the cooking processes in our kitchen are isobaric processes , when the food is cooked in an open vessel the pressure above the food is always at atmospheric pressure
The PV diagram for an isobaric process is a horizontal line parallel to volume axis figure (a) represents isobaric proceess where decreases figure (b) represents isobaric process where volume increases
The work done in an isobaric process : work done by the gas
` W= int_(v_1)^(v_f)pd V `
In an isobaric process the pressure is constant , so P comes out of the integral
` W= P int_(v_i)^(v_f) dV `
` W=P[V_f -V_i]=P Delta V `
Where `Delta V ` denotes change in the volume .IF `Delta V ` is negative ,W is also negative this implies that the work is done on the gas .If ` Delta V ` is positive , W is positive W is also positive implying that work is done by the gas .
The equation (6) can also be rewritten using the ideal gas equation .
from ideal gas equation
` PV = mu RT and V =( mu RT )/(P )`
Substituting this in equation ( 6) we get
`W = mu RT _f (1- (T_i )/(T_f ))`
in the PV diagram , area under the isobaric curve is equal to the work done is isobaric process .
The first law of thermodynamics for isovaric process is given by
` Delta U = Q- P Delta V `
` W = P Delta V , Delta U = Q - mu RT _f [ 1-(T_i )/(T_f)]`
