Entropy change in an ideal gas - Find the entropy change of an n mole of...

  

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Entropy change in an ideal gas - Find the entropy change of an n mole of an ideal gas in a reversible process from a state A (PA, VA, TA) to a state B (PB,VB,TB). Specific heats cy and cp are given. 2. Response functions Show that kr(Cp Cy) TVα² and Cp(kr ks) TVα² Here the compressibility is given by Kx = -(1/V)(avp)x and the coefficient of thermal expansion is a = (1/V) (A/T). 3. Thermodynamic stability of rubber bands and Gibbs- Duhem - One can experimentally verify quite easily that a rubber band heats up when it is stretched adiabatically. (a) Given this fact, will a rubber band contract or expand when it is cooled at constant tension? (b) The same amount of heat flows into two identical rubber bands, but one is held at constant tension, and the other one at constant length. Which one has the largest increase in temperature? (c) Suppose the rubber band satisfies the equation of state U = 0S²L n² with 0 being a constant. Determine the chemical potential of the system μ(T, I) and show explicitly that potential of the system μ(T, I) and show explicitly that the equation of state satisfies the relevant Gibbs- Duhem relation from the tutorials. 4. Stability of magnetic systems - Consider a magnet with magnetization M in the direction of the magnetic field strength H. In appropropriate units the work is given by HdM. (a) Determine the signs of the isothermal and adiabatic susceptibilities, XT= = әм = (OH) T T,n,V әм Xs= Ән S,n,V Furthermore, determine the sign of XT - XS (b) Suppose a paramagnetic substance has a decreasing magnetization as function of temperate at constant H. Will the temperature increase or decrease when the material is adiabatically demagnetized? 5. Generalised Euler theorem - Given the generalised homogeneous function f(x1,xn) = f (x1,...,xn) with 0i a real number for i = 1,..., n. Show that af af 012 + +Anan = f(x1,...,xn) дх 21-1 22 This generalisation of Euler's theorem plays an important role in the theory of phase transitions close to the critical point. Entropy change in an ideal gas - Find the entropy change of an n mole of an ideal gas in a reversible process from a state A (PA, VA, TA) to a state B (PB,VB,TB). Specific heats cy and cp are given. 2. Response functions Show that kr(Cp Cy) TVα² and Cp(kr ks) TVα² Here the compressibility is given by Kx = -(1/V)(avp)x and the coefficient of thermal expansion is a = (1/V) (A/T). 3. Thermodynamic stability of rubber bands and Gibbs- Duhem - One can experimentally verify quite easily that a rubber band heats up when it is stretched adiabatically. (a) Given this fact, will a rubber band contract or expand when it is cooled at constant tension? (b) The same amount of heat flows into two identical rubber bands, but one is held at constant tension, and the other one at constant length. Which one has the largest increase in temperature? (c) Suppose the rubber band satisfies the equation of state U = 0S²L n² with 0 being a constant. Determine the chemical potential of the system μ(T, I) and show explicitly that potential of the system μ(T, I) and show explicitly that the equation of state satisfies the relevant Gibbs- Duhem relation from the tutorials. 4. Stability of magnetic systems - Consider a magnet with magnetization M in the direction of the magnetic field strength H. In appropropriate units the work is given by HdM. (a) Determine the signs of the isothermal and adiabatic susceptibilities, XT= = әм = (OH) T T,n,V әм Xs= Ән S,n,V Furthermore, determine the sign of XT - XS (b) Suppose a paramagnetic substance has a decreasing magnetization as function of temperate at constant H. Will the temperature increase or decrease when the material is adiabatically demagnetized? 5. Generalised Euler theorem - Given the generalised homogeneous function f(x1,xn) = f (x1,...,xn) with 0i a real number for i = 1,..., n. Show that af af 012 + +Anan = f(x1,...,xn) дх 21-1 22 This generalisation of Euler's theorem plays an important role in the theory of phase transitions close to the critical point.