--%>
Assignment Help - homework help

Problem on Adiabatic expansion

Calculate the change in entropy for the system for each of the following cases. Explain the sign that you obtain by a physical argument

a) A gas undergoes a reversible, adiabatic expansion from an initial state at 500 K, 1 MPa, and 8.314 L to a final volume of 16.628 L.

b) One mole of methane vapor is condensed at its boiling point, 111 K; Δhv = 8.2 [kJ/mol].

c) One mole of liquid water is cooled from 100°C to 0°C. Take the average heat capacity of water to be 4.2 JK-1g-1.

d) Two blocks of the same metal with equal mass are at different temperatures, 200°C and 100°C. These blocks are brought together and allowed to come to the same temperature. Assume that these blocks are isolated from their surroundings. The average heat capacity of the metal is 24 JK-1mol-1.

E

Expert

Verified

(a) Since the heat transfer, ΔQ = 0, in reversible adiabatic process, the entropy change,

ΔS = ΔQ/T = 0

(b) ΔS = Δhv/T = (-8.2 kJ/mol)/111 K = -0.074 kJ/(mol.K) = -74 J/(mol.K)

Since one mol is condensed, -74J/K is the entropy change, and this heat taken up by surrounding whose entropy change is positive 74J/K, and hence the entropy change of system plus surrounding is zero, in confirmation with the second law of thermodynamics.

(c) ΔS = ΔQ/T = ∫cp,avgdT/T = cp,avg ∫dT/T = cp,avg ln (T2/T1) = 4.2 ln(273/373) = = -1.31 J/(gK).

But we have 1 mol of water, i.e. 18 gm of water. Hence ΔS = -1.31 x 18 = -23.58 J/K

The negative sign implies that heat is lost or transferred from system to surrounding.

In other words water is cooled, by transferring the heat, hence the change in entropy is negative, while the surrounding gain the same amount of heat and for it the change in entropy is positive, hence the total change in entropy is zero, i.e. System + Surroundings.

(d) Let the equilibrium temperature be T,

mCp(200 – T) = mCp(T – 100)
(200 – T) = (T – 100)
T = 150oC

Total change in entropy of the system,

        = change in entropy of 1st block + change in entropy of 2nd block

        = cp ln (T2/T1) + cp ln (T2/T1)

        = 24ln (423/473) + 24ln (423/373)

        = 0.338 J/mol.K

Thus the entropy change is positive in this case, implying there are more configurations when the two blocks are allowed to interact.

   Related Questions in Chemistry

  • Q : Describe the properties of the

    Briefly describe the properties of the carbohydrates?

    		•
  • Q : Henry law question Answer the following

    Answer the following qustion. The definition “The mass of a gas dissolved in a particular mass of a solvent at any temperature is proportional to the pressure of gas over the solvent” is: (i) Dalton’s Law of Parti

    		•
  • Q : Problem related to molarity Provide

    Provide solution of this question. Increasing the temperature of an aqueous solution will cause: (a) Decrease in molality (b) Decrease in molarity (c) Decrease in mole fraction (d) Decrease in % w/w

    		•
  • Q : Molarity of pure water Choose the right

    Choose the right answer from following. The molarity of pure water is: (a) 55.6 (b) 5.56 (c)100 (d)18

    		•
  • Q : What is heat capacity and how to

    The temperature reliance of internal energy and enthalpy depends on the heat capacities at constant volume and constant pressure. The internal energy and enthalpy of chemical systems and the energy changes that accompany chemical reactions depend on the

    		•
  • Q : Problem on vapor-liquid equilibrium Two

    Two tanks which contain water are connected to each other through a valve. The initial conditions are as shown (at equilibrium): 683_tank question.jpg

    		•
  • Q : Problem on Adiabatic expansion

    Calculate the change in entropy for the system for each of the following cases. Explain the sign that you obtain by a physical argument a) A gas undergoes a reversible, adiabatic expansion from an initial state at 500 K, 1 MPa, and

    		•
  • Q : What is solvent dielectric effect?

    Ionic dissociation depends on the dielectric constant of the solvent.The Arrhenius that ions are in aqueous solutions in equilibrium with parent molecular species allows many of the properties of ionic solutions to be understood. But difficulties began to

    		•
  • Q : Calculating total vapour pressure

    Select the right answer of the question. The vapour pressure of two liquids P and Q are 80 and 600 torr, respectively. The total vapour pressure of solution obtained by mixing 3 mole of P and 2 mole of Q would be: (a) 140 torr (b) 20 torr (c) 68 torr (d) 72 torr

    		•
  • Q : Explanation of oxygen family. Group 16

    Group 16 of periodic

    		•