Thermodynamics | Polytropic Process#
Polytropic Process#
- Polytropic process is a process which follows the equation:
where, x = polytropic index and k = constant
Special Cases:
- If x = 0 ⇒ P = constant ⇒ Isobaric process
- If x = 1 ⇒ PV = constant ⇒ Isothermal process
- If x = γ ⇒ PVγ = constant ⇒ Adiabatic process
Work done in a polytropic process#
For a reversible polytropic process, work done can be calculated as:
Calculation of molar heat capacity#
- Molar heat capacity is defined as heat capacity per unit mole.
- Let's calculate dV/dT so that it can be used in above expression.
Differentiating both sides:
Putting in the expression of Cm:
Since, PV = nRT (ideal gas equation), we can write:
Questions based on Polytropic Process#
For a monoatomic ideal gas, the ratio of pressure and square of volume is 3. How much heat should be supplied to increase the temperature of 5 moles of the gas by 50oC?
This is a polytropic process with x = -2.
Molar heat capacity is given by:
Also, molar heat capacity is given by:
The molar heat capacity of a gas (at room temperature) for which pressure and volume are equal is 7R/2. What will be the rotational degree of freedom for this gas? Also, predict the atomicity of gas.
This is a polytropic process with x = -1.
Molar heat capacity is given by:
Thus, it is a triatomic gas.
Thus, total degree of freedom = 6
Let ftr = Translational degree of freedom and fr = Rotational degree of freedom. Then, At room temperature:
Thus, rotational degree of freedom is 3.
Calculate the molar heat capacity of monoatomic gas for which the ratio of pressure and volume is 1.
This is a polytropic process with x = -1.
Molar heat capacity is given by:
Since, Cv = 3R/2 for a monoatomic gas, we can write: