Question

What is an isobaric process? Obtain the expressions for the work done, change in internal energy and heat supplied in an isobaric process in the case of a gas.

Answer 1

A process in which pressure remains constant is called an isobaric process. Consider n moles of a gas enclosed in a cylinder fitted with a movable, massless and frictionless piston. We assume that the gas behaves as an ideal gas so that we can use the equation of state PV = nRT.

Consider an isobaric expansion (or compression) of the gas in which the volume of the gas changes from V_i to V_f and the temperature of the gas changes from T_i to T_f when the pressure (P) of the gas is kept constant. The work done by the gas,

Now, PV_i = nRT_i and PV_f = nRT_f

∴ PV_f – PV_i = nRT_f – nRT_i

∴ P(V_f – V_i) = nR(T_f – T_i) 

∴ from Eq. (1), W = nR(T_f – T_i) … (2) 

The change in the internal energy of the gas, 

∆ U = nC (T – T ) …(3)

where C_v is the molar specific heat of the gas at constant volume.

From Eqs. (2) and (3), 

we have, the heat supplied to the gas,

Q = ∆ U + W = nC_v (T_f – T_i) + nR(T_f – T_i)

= n(C_v + R)(T_f – T_i) 

∴ Q = _nC_p (T_f – T_i) …(4) 

Where C_p ( = C_v + R) is the molar specific heat of the gas at constant pressure. 

[Note : P-V curve for an isobaric process is called an isobar.