We know,
Q = W + ΔU
For constant pressure process,
W = Q - ΔU
W = (5/2 - 3/2) * nR ΔT
W = nR ΔT
For Adiabatic Process, Q = 0
So,
W + ΔU = 0
ΔU = - W
ΔU = 3/2 nR ΔT
For Constant Volume process, W = 0
Q = W + ΔU
Q = ΔU
ΔU = 3/2 nR ΔT
For Isothermal Process, ΔU = 0
So,
Q = W
Q = nRTln(vF/vI)
The following table lists results for various processes involving n moles of a monatomic ideal gas....
A sample of n moles of a monatomic ideal gas is expanded isothermally and reversibly at a constant temperature T from a volume V to 3V. Note that since the temperature of the gas is constant, the internal energy will remain constant. a) Write an expression for the change in entropy ΔS for the system. b) The sample has 7 moles of gas and is kept at a temperature of 305 K. The volume is changed from 0.065 m3 to...
The Sackur-Tetrode Equation gives the entropy of a sample of n moles of monatomic ideal gas as a function of its internal energy U and volume V S(U, V) = 5/2 n R + n R In (V/n N_A(4piM U/3nN^2_Ah^2)^3/2) In the equation, R is the gas constant, M is the molar mass, N_4 is Avogadro's number, and h is Plank's constant. The equation can be derived using S = k ln W and directly computing W, the number of...
Consider n moles of ideal gas kept in a heat-isolated cylinder (all processes are adiabatic) with a piston at external pressure p0, and at temperature T0. The external pressure is suddenly changed to p=2p0, and we wait for the system to equilibrate. The volume and the temperature of the ideal gas after equilibration is V and T, respectively. a) Calculate the amount w of work produced on the system in terms of p, p0, V, T0, and n. Using the...
TB4 The PV diagram in the figure is for n moles of an ideal monatomic gas. The gas is initially at point A. The paths AD and BC represent isothermal changes. R is the universal gas constant. Let the pressures, volumes, and temperatures at the labeled points be denoted as PA , PB, etc., and VA , VB, etc., and TA, TB, etc., respectively. If the system is brought to point C along th<e path A-»E->C, what is the heat...
Ten. moles of ideal gas (monatomic), in the initial state P1=10atm, T1=300K are taken round the following cycle: a. A reversible isothermal expansion to V=246 liters, and b. A reversible adiabatic process to P=10 atm c. A reversible isobaric compression to V=24.6 liters Calculate the change of work (w), heat (q), internal energy (U), and entropy (S) of the system for each process?
A Piston-cylinder heat engine containing a monatomic ideal gas
undergoes the three processes drawn on the p-V diagram below. The
gas is initially at room temperature (300 K). Determine the total
work done by the gas, and the total heat flow into the gas after
completing one cycle. What is the thermal efficiency of this
engine?
Problem Statement A piston-cylinder heat engine containing a monatomic ideal gas undergoes the three processes drawn on the p-V diagram below. The gas is...
PROBLEM 1: (50 pts) Consider the following isothermal monatomic ideal gas expansion processes: gradual (reversible) decrease in pressure from P, to Pa, such that the internal and external pressures remain in equilibrium at every step along the path. a) (20 pts) Obtain expressions for AU, W, AS, and Au for the above process (express your results as functions of n, T, P, and/or P2) b) (10 pts) Calculate the work exchanged (in J) in the process, assuming that n=1 mole,...
4. A heat engine contains an ideal monatomic gas confined to a cylinder by a movable piston. The gas starts at point A shown in the figure, where T 3.00 x102 K. The process B C is an isothermal expansion. (a) Find the number of moles of the gas and the temperature at point B. (b) Find AU, Q (the heat flow), and W (the work done by the system) for the isovolumetric process A B, (c) the isothermal expansion...
Two moles of a monatomic ideal gas goes through the cycle
represented in Figure below. TA=420 K; VA=0.025 m3 and VB=0.045 m3
. R=8.314 J/mol K.
a) Identify the process A-B, B-C and C-A (3)
b) Calculate PA , PB and TC , the pressures and temperature
reached in A,B and C. [9 marks]
c) Complete the following table (on a separate document to be
attached). Detail your work. [30 marks]
i) A-B (8)
ii) B-C (8)
iii) C-A...
B.2 The multiplicity of a monatomic ideal gas is given by 2 = f(N)VN U3N/2, where V is the volume occupied by the gas, U its internal energy, N the number of particles in the gas and f(N) a complicated function of N. [2] (i) Show that the entropy S of this system is given by 3 S = Nkg In V + ŽNkg In U + g(N), where g(N) is some function of N. (ii) Define the temperature T...