Heat capaticy of isobaric process with real gas

Therefore, an isobaric process is a special case of a polytropic process with n = 0. If the gas is ideal, then n = 0. Therefore, an isobaric process is a general polytropic process for an ideal gas. If the gas is not ideal, then n may not equal 0, but the process is still considered polytropic. It is defined by the equation $$c \mathrm{d}T = \mathrm{\delta}Q$$ where c is constant. This can be further defined for an isobaric process as $$c_P=\left(\frac{\mathrm{d}Q}{\mathrm{d}T}\right)_P$$ where c_P is the specific heat
  • #1
lakmus
23
1
Hey,
during last lecture of thermodynamics we did polytropic processes, and with no
discuss teacher said, that isobaric process is in general polytropic. If we had ideal
gas, then it is clear, bud what if the gas isn't ideal?
I tried to proof it, but I stuck and don't know how to continue.
If I write the definition of polytropic process
[itex]c \mathrm{d}T = \mathrm{\delta}Q[/itex], where [itex]c[/itex] must be constant. For isobaric process we have
[itex]c_P = \left(\frac{\mathrm{d}Q}{\mathrm{d}T}\right)_P[/itex], where index right down the derivation notes what state variable is constant. To define the state in thermodynamics, we
need just two state variable, so
[itex]c_P = \left(\frac{\mathrm{d}U(P,T)}{\mathrm{d}T}\right)_P + \left(\frac{P\mathrm{d}V
(P,T)}{\mathrm{d}T}\right)_P[/itex]. And know I don't know how to continue. I tried said that
[itex]U(T,V(P,T))[/itex] and chain rule, but it didn't look better . . .
Thanks for any help . . .
 
Last edited:
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  • #2
In an isobaric process, $$Q=\Delta H = C_p \Delta T$$. Also, for a polytropic process, $$PV^n=constant$$For an isobaric process, n = 0.
 

1. What is heat capacity?

Heat capacity is the amount of heat required to raise the temperature of a substance by one degree. It is typically measured in joules per kelvin (J/K) or calories per degree Celsius (cal/°C).

2. What is an isobaric process?

An isobaric process is a thermodynamic process in which the pressure of a system remains constant, while other parameters such as volume and temperature may change. This type of process is often seen in open systems, where the system has a constant pressure due to interactions with its surroundings.

3. How does heat capacity vary with pressure in an isobaric process?

In an isobaric process, the heat capacity of a substance can vary with pressure. This is because the pressure can affect the intermolecular forces and therefore the energy required to change the temperature of the substance. In general, as pressure increases, the heat capacity of a substance will also increase.

4. Can the heat capacity of a real gas be accurately calculated?

The heat capacity of a real gas can be accurately calculated using the Mayer equation, which takes into account the rotational and vibrational degrees of freedom of the gas molecules. However, for many real gases, this equation may not be accurate enough and experimental measurements may be necessary.

5. How does the heat capacity of a real gas differ from an ideal gas?

The heat capacity of a real gas differs from an ideal gas because real gases have more complex intermolecular interactions, such as van der Waals forces, which affect the energy required to change the temperature of the gas. In contrast, ideal gases have no intermolecular forces and therefore have a constant heat capacity regardless of pressure or temperature.

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