Principles of Thermodynamics 1st. Edition by Jean-Philippe Ansermet, Sylvain D. Brechet | 9781108426091 | 1108426093 | Holooly

Principles of Thermodynamics [EXP-7769]

166 SOLVED PROBLEMS

Question: 6.11.5

1. Determine the expression of the internal energy U(T, V) of the van der Waals gas, assuming that the specific heat at constant volume CV is independent of temperature. 2. Show that during a Joule expansion, where the volume of gas increases while the system is isolated, the temperature T of the

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1. Using Maxwell relation (4.71) and the van der W...

Question: 10.2

1. Determine the expression of the pressure time derivative. 2. Determine the expression of the pressure gradient.

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1. Taking into account equations (10.86) and (10.7...

Question: 1.10.1

1. Establish relation (1.18) in which the velocity v is the intensive quantity conjugated to the momentum P. 2. Establish relation (1.21) in which that the angular velocity ω is he intensive quantity conjugated to the angular momentum L.

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Using the momentum definition (1.16), P = Mν, the ...

Question: 6.11.1

1. Perform a second-order series expansion with respect to ΔU and ΔV and show that the global condition for the concavity of entropy (6.9) as a function of internal energy and volume can be expressed as ∂^2S/∂U^2 ΔU^2 + 2 ∂^2S/∂U∂V ΔUΔV +∂^2S/∂V^2 ΔV^2 ≤ 0. 2. Take into account the local concavity

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The global condition for the concavity of entropy ...

Question: 2.11.1

1. Show that the evolution equation of a harmonic oscillator of mass M, subjected to an elastic force Fel = −k r and free of friction, is invariant under time reversal. 2.Demonstrate that the evolution equation of a damped harmonic oscillator of mass M, subjected to an elastic force Fel = −k r and a

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1. According to the definition (1.16) of momentum,...

Question: 1.6

A basin contains Ns (t) moles of salt dissolved in Nw (t) moles of water. The basin receives fresh water at a constant rate Ω^in w . This water is assumed to be thoroughly mixed in the basin so that the salt concentration can be considered homogeneous. The salty water comes out of the basin at a

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The time derivative of the amount of salt in the b...

Question: 5.2

A bicycle pump takes a volume ΔV of air at atmospheric pressure p0 and constant temperature T0 and compresses it so that it enters a tire that has a volume V0. The air inside the tire is initially at atmospheric pressure p0 and can be considered as an ideal gas.Determine the number of times n the

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The initial and final number of moles of air insid...

Question: 11.14

A biological medium consists of two substances 1 and 2 of densities n1 and n2. This medium is generating both substances by processes characterised by the matter source densities π1 (n1, n2) and π2 (n1, n2). The substances 1 and 2 can diffuse inside this medium. The matter current densities j1 and

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a) Using the definition (10.25) for the matter sou...

Question: 4.8.1

A black body is an object at equilibrium with the radiation it emits. This radiation is characterised by the fact that the internal energy density depends only on the temperature at thermal equilibrium. The internal energy of this radiation is given by, U(S,V)=3/4(3c/16σ)^1/3S^4/3V^−1/3.

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1. The black body temperature (2.9) is defined as,...

Question: 8.10

A container at a pressure p and temperature T contains two substances 1 and 2, present both in liquid and gas phases. Estimate the partial pressure pA of substance A in the gas phase (A = 1, 2) as a function of the concentrations cl1 and cl2 of substances 1 and 2 in the liquid phase. Raoult’s law

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The chemical potentials of substance A in the liqu...

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