Chapter 10

Thermodynamics

To test the understanding of the lesson

Question

  • Give the differential expression of mass internal energy of an ideal gas.

  • Give the differential expression of mass internal enthalpy of an ideal gas.

  • What is the integral expression of the entropy of an ideal gas in terms of the and variables ?

Hint

Solution

  • Differential of mass internal energy of a perfect gas :

  • Differential of the mass internal enthalpy of an ideal gas :

  • Molar entropy of an ideal gas in terms of the variables then  :

Question

What is the differential expression of the elementary work pressure forces received by a closed system in the general case and in the case of a reversible transformation ?

Hint

Solution

In the general case, noting  :

If the transformation is reversible, and :

 

Question

What is the work received by one mole of an ideal gas in a reversible isothermal transformation ?

Hint

Solution

If the transformation is reversible isotherm :

And :

In the case of an expansion, and  : the external environment gets back work.

Question

  • Give the ideal gas equation of state in intensive variables , and (density).

  • Give the equation of state of an ideal gas using the Boltzmann constant and particle density .

  • What is the gas state equation of Van der Waals for moles, in variables , and  ?

Hint

Solution

  • Ideal gas equation of state in intensive variables , and  :

    ( is the molar mass)

  • Equation of state of an ideal gas using the Boltzmann constant and particle density  :

  • Gas state equation of Van der Waals for moles, in variables , and  :

Question

What is an ideal gas ?

Hint

Solution

  • At the macroscopic scale : a perfect gas is a (real !) gas studied at low pressures (less than a few bars, is normal atmospheric pressure).

  • At the microscopic scale : the particles of an ideal gas are punctual and do not interact with each other but only with the wall of the container they occupy during elastic collisions.

Question

Give the value of the quadratic (RMS) speed of a perfect mono-atomic gas. What is its order of magnitude ?

Hint

Solution

The root mean square velocity of a perfect mono-atomic gas :

Where is the mass of a particle, the molar mass, the Boltzmann constant and perfect gas constant.

Order of magnitude :

For Argon, at , .

For Helium, at , .

Question

Express molars capacity and of an ideal gas in terms of (gas constant) and .

Hint

Solution

Question

Give the differential formulation of the first law of thermodynamics for a closed system in its most general form.

Hint

Solution

Noting the internal energy, macroscopic gravitational potential energy and the macroscopic kinetic energy :

Where and are the work and heat transfer received by the closed system.

Question

Give the differential formulation of the second law of thermodynamics for a closed system (system macroscopically at rest).

Hint

Solution

With :

Question

Give the first thermodynamic identity, in differential form ( relationship between , , , and ).

Hint

Solution

Question

Leave the second thermodynamic identity, in differential form (relationship between , , , and ).

Hint

Solution

Question

  • How to calculate heat transfer during a transformation at a constant volume ?

  • How to calculate heat transfer during a transformation at constant external pressure ?

Hint

Solution

  • A constant volume :

  • A constant external pressure :

Question

To state the theorem of Carnot on ditherme machines.

Hint

Solution

Note and the temperatures of the cold source and the hot source.

For a dithermal machine operating irreversibly, the yield is still lower than that obtained during a reversible operation :

Question

Give the relationship between and , and between and , and finally between and for isentropic evolution of an ideal gas of constant ratio .

Hint

Solution

They write the laws of Laplace :

Question

State the "first industrial valid law" for flowing fluids in industrial machines.

Hint

Solution

Using mass quantities :

Question

What is the statistical interpretation of entropy ?

Hint

Solution

Entropy is related to the molecular disorder. The greater entropy of a system, the more disorder.

Thus, the entropy of a pure substance from a liquid to a gaseous state increases.

Question

An electronic pulse generator emits pulses of energy , each at the frequency of .

The efficiency of the generator is equal to %.

How many liters of water per minute circulate in the cooling system of the generator so that the water temperature at the output does not increase by more than ?

The specific heat capacity of water is :

.

Hint

Solution

In a period , energy given par the generator is .

For the water :

So :

.

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Reversible adiabatic oscillations