--%>
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 Thermodynamics Properties The

    The free energy property leads to convenient expressions for the volume and pressure dependence of internal energy, enthalpy and the heat capacities.All the properties of a chemical system, a sample of a substance, or a mixture of substances have some fixe

    		•
  • Q : Molarity 20mol of hcl solution requires

    20mol of hcl solution requires 19.85ml of 0.01 M NAOH solution for complete neutralisation. the molarity of hcl solution

    		•
  • Q : Thermodynamics I) Sulphur dioxide (SO2)

    I) Sulphur dioxide (SO2) with a volumetric flow rate 5000cm3/s at 1 bar and 1000C is mixed with a second SO2 stream flowing at 2500cm3/s at 2 bar and 200C. The process occurs at steady state. You may assume ideal gas behaviour. For SO2 take the heat capacity at constant pressure to be CP/R = 3.267

    		•
  • Q : Problem on convection coefficient An

    An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves insertion of thermocouples in the casting at distances of 10 mm and 20 mm from the surface.  When the experiment was perform

    		•
  • Q : Modes of concentration Which of the

    Which of the given modes of expressing concentration is fully independent of temperature: (1) Molarity (2) Molality (3) Formality (4) Normality Choose the right answer from above.

    		•
  • Q : Molar mass what is the equation for

    what is the equation for calculating molar mass of non volatile solute

    		•
  • Q : What is synthetic rubber and how it

    To meet human needs, scientists have started preparing synthetic rubbers. Besides having similar properties as natural rubbers they are tougher, more flexible and more durable than natural rubber. They are capable of getting stretched to twice its length. Though, it reverts to its original shape

    		•
  • Q : Theory of one dimensional motion For

    For motion in one dimension, the distribution of the molecules over quantum states, speeds, and energies can be deduced.Here we show that the energy of a macroscopic gas sample can be described on the basis of our knowledge of the quantum states allowed to

    		•
  • Q : Partial vapour pressure of volatile

    Choose the right answer from following. For a solution of volatile liquids the partial vapour pressure of each component in solution is directly proportional to: (a) Molarity (b) Mole fraction (c) Molality (d) Normality

    		•
  • Q : Explain the catalyst definition and

    Catalyst is a substance which accelerates the rate of a chemical reaction without undergoing any change in its chemical composition or mass during the reaction. The phenomenon of increasing the rate of a reaction with the help of a catalyst is known as catalysis.

    		•