MCP 1 Chapter 1 Thermodynamics
Questions about the lecture 'From Molecular to Continuum Physics 1' of the RWTH Aachen Chapter 1 Thermodynamics
Questions about the lecture 'From Molecular to Continuum Physics 1' of the RWTH Aachen Chapter 1 Thermodynamics
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Lernkarten
What is the definition of electrical work?
dw = Phi*dQ with potential Phi [V] and change of charge dQ [C]
What is the definition of adiabatic work?
Due to work T decreases with DU = C_V*DT = w_ad
What is the definition of reversibility of work? [2]
1. Change that can be reversed by an infinitesimal modification
2. Possible if in equilibrium with p_ex = p=nRT/V and w=nRT*ln(Vf/Vi)
What heat capacities exist? [5]
1. Volume C_V = (dU/dT)_V
2. Molar C_Vm = C_V/n is intensive
3. Specific C_Vs = C_V/m
4. Pressure C_P = (dH/dT)_p is extensive
5. Molar C_Pm = C_P/n is intensive
What are the characteristics of volume heat capacity? [2]
1. Extensive property
2. Relation between change in internal energy and change in temperature
What holds for volume and pressure heat capacity?
C_P-C_V = nR = alpha*(p+pi_T)*V // C_P larger than C_V
What is the first law of thermodynamics TD1? [2]
1. “The internal energy of an isolated system is constant.”
2. dU = dq + dw
How is the differential form of TD1 defined? [2]
1. DeltaU = q+w
2. dU = dq + dw with dw = dw_exp+dw_e and dw_e extra work
What holds for isolated systems and q=w=0?
U constant
What holds for dw_exp=0? [3]
1. V constant dw_e also zero and dU=dq
2. dU=C_V*dT
3. DU=C_V*DT if C_V dependent on T
What are characteristics for w and q? [1]
w and q are properties of the path and not the state
What is the definition of the acquisitive connection? [2]
1. w or q are positive if energy is transferred to the system
2. w or q are negative if energy is transferred out of the system
What is the definition of the internal pressure? [2]
1. pi_T = (dU/dV)_T
2. Is zero for perfect gas? // Joules experiment
What is the definition of the expansion coefficient? [3]
1. alpha = 1/V * (dV/dT)_P
2. How strongly does the system responds to changes of T
3. Is 1/T for perfect gas
What is the definition of the isothermal compressibility? [2]
1. k_T = - 1/V*(dV/dp)_T
2. Is 1/p for perfect gas
What holds in a closed system U(V,T)? [2]
1. dU = pi_T*dV + C_V*dT
2. dU/dT = pi_T* (dV/dT)_P + C_V with (dV/dT)_P = alpha*V
What is the definition of enthalpy? [4]
1. H = U + pV with dH=dq and DH=qP
2. Energy supplied as heat at constant pressure
3. State function due to state functions U p and V
4. dH = (dH/dp)_T*dp + (dH/dT)_p*dT = C_P*(mye*dp + dT) [what happened with -C_P)
What is the definition of joule-thomson?
mye = (dT/dp)_H
What are the characteristics of joules experiment? [2]
1. Measure pi_T by observing dT of a gas expanding into vacuum
2. Observations are w=0 q=0 → dU=0 and pi_T=0
What is the second law of thermodynamics TD2? [2]
1. “The entropy of an isolated system increases due to spontaneous change.”
2. TdS = dq_rev
What is definition of entropy? [5]
1. Disorder or energy dispersed in a process influenced by heat
2. State function for the accessibility of a state by a spontaneous change
3. Always positive (irreversible) or zero (reversible) but never negative
4. Measured by the temperature
5. Direction of natural change
What are the formulae of entropy? [6]
1. dS = dq_rev/T with q_rev [J/K] reversibly supplied heat
2. DS = integral_i,f(dq_rev/T)
3. DS = nR*ln(Vf/Vi) for isothermally gas expansion
4. DS = C_P*ln(Tf/Ti) for isobaric processes
5. dS = DS = dq_sur/T_sur for the surroundings
6. DS = 0 for adiabatic changes
What is the definition of spontaneous change? [3]
1. Opposite of random motion // Gas does not change spontaneously
2. Irreversible processes
3. Increase S_tot
What is the definition of the clausius inequality? [2]
1. dS \geq dq/T
2. Is a system reversible or not?
What is the definition of the fundamental equation of internal energy? [3]
1. With no additional (non-expansion) work dw_rev=-pdV
2. dU op TdS – pdV // Reversible if op is = and irreversible if op is <
3. Temperature is the ratio of dU and dS for a constant V / Pressure is the ratio of dU and dV for a constant S
What is the third law of thermodynamics TD3 or Nerst heat theorem? [2]
1. “The entropy of a system at zero is a universal constant.”
2. T=0 → S=0
What are the criteria for spontaneous change in thermal equilibrium under constant volume? [5]
1. dU=dq_V → TdS \geq dU
2. Solely in terms of the state functions
3. If internal energy is constant then entropy increases
4. If entropy is constant then internal energy decreases and entropy of the surroundings increases
5. Decrease of helmholtz free energy
What are the characteristics of helmholtz free energy? [4]
1. dA = dU-TdS
2. dA = dw_max // Part of internal energy which is free to do work with
3. If entropy decreases then heat flows out to increase the entropy of the surroundings
4. If entropy increases then heat flows in to decrease the entropy of the surroundings
What are the criteria for spontaneous change in thermal equilibrium under constant pressure? [4]
1. dH=dq_P → TdS \geq dH
2. If enthalpy is constant then entropy increases
3. If entropy is constant then enthalpy decreases and entropy of the surroundings increases
4. Decrease of gibbs free energy
What are the characteristics of gibbs free energy? [7]
1. dG = dH-TdS
2. dG = dw_add,max
3. dG = Vdp – SdT // Fundamental equation of chemical thermodynamics
4. (dG/dT)_p = -S = G-H/T
5. (d(DG/T)/dT)_p = -DH/T¹
6. For solids and liquids independent of pressure // Vm constant and possible to neglect
7. For gas Gm(pf)=Gm(pi) + RT*ln(pf/pi) with Gm molar gibbs energy
What is the definition of the kelvin-planck statement? [3]
1. It is impossible to transform Q_H completely into W
2. An amount Q_C flows into the environment
3. Efficiency = W/Q_H with W = Q_H-Q_C
What it the definition of the molecular view on entropy? [2]
1. S = k*ln(W) with W number of equivalent ways of describing system
2. Dependent of temperature with T=0 → W=1 and S=0 // localization of matter
What is the definition of a multivariate calculus? [2]
1. df = g*dx + h*dy with f(x,y), g(x,y) and h(x,y)
2. (dg/dy)_x = d²f/dydx = (dh/dx)_y // If both exist and continuous
What are the characteristics of the maxwell relations? [3]
1. In closed system
2. With constant composition
3. Only expansion work
What are the maxwell relations? [4]
1. (dT/dV)_S = -(dp/dS)_V for U
2. (dT/dp)_S = (dV/dS)_p for H
3. (dp/dT)_V = (dS/dV)_T for A
4. (dV/dT)_P = -(dS/dp)_T for G
