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Sph 302 : Thermodynamics Question Paper

Sph 302 : Thermodynamics

Course:Bachelor Of Education (Science)

Institution: Jaramogi Oginga Odinga University Of Science And Technology question papers

Exam Year:2017

JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND TECHNOLOGY SCHOOL OF BIOLOGICAL AND PHYSICAL SCIENCES
UNIVERSITY EXAMINATION FOR THEDEGREE OF BACHELOR OF EDUCATION (SCIENCE)
3RDYEAR 1STSEMESTER
MAIN
REGULAR

COURSE CODE: SPH 302
COURSE TITLE: THERMODYNAMICS
EXAM VENUE: STREAM: (BED SCI)
DATE: EXAM SESSION:
TIME: 2:00HRS
________________________________________________________________________
Instructions:
Answer question 1 (Compulsory) and ANY other 2 questions.
Candidates are advised not to write on the question paper.
Candidates must hand in their answer booklets to the invigilator while in the examination room.
TaketheIdeal-gas constant,R to be8.3145J/(mol.K)
QUESTION ONE (30 Marks)
For an ideal monatomic gas of one mole, calculate the heat capacity at a constant pressure, Cp
(2 marks)
Show that, for an ideal gas
(i) R/C_v =?-1(2 marks)
(ii) R/C_P =(?-1)/?where R is an ideal-gas constant, Cv and Cp are the heat capacities per mole and ? is the adiabatic index. (2 marks)
Use thermodynamic arguments to obtain the general result that, for any gas at temperature T, thepressure is given by
where U is the total energy of the gas.(3 marks)

In an adiabatic change, show that
(6 marks)
What is the maximum possible efficiency of an engine operating between two thermal reservoirs, one at 100?C and the other at 0?C? (2 marks)
What is the change of entropy in the gas, surroundings and Universe during a Joule expansion?(2 marks)
Suppose 1.00 kg of water at 100°C is placed in thermal contact with 1.00 kg of water at 0°C. Find the approximate total change in entropy when the hot water cools to 99°C and the cold water warms to 1°C.Assume that the specific heat capacity of water is constant at over the given temperature range.(3 marks)
Summarize three main consequences of the third law of thermodynamics and explain how it casts a shadow of doubt on some of the conclusions from various thermodynamic models.
(6 marks)
(i) Show that in phase equilibrium, each coexisting phase has the same chemical potential µ_1=µ_2(2 marks)

QUESTION TWO (20 Marks)
One mole of ideal monatomic gas is confined in a cylinder by a piston and is maintained at a constant temperature 80ocby thermal contact with a heat reservoir. The gas slowly expands from Vto 2Vwhile being held at the same temperature.
Explain why does the internal energy of the gas not change?(2 marks)
Calculate the work done by the gas (3 marks)
The heat flow into the gas. (3 marks)
For an ideal monatomic gas of one mole
Show that for, the gas constant, R at constant pressure is given byR=P(?V/?T)_pwhere p, V and T have their usual meanings. (3 marks)
(ii) Calculate the molar heat capacity of the gas at a constant volumeCV.(3 marks)
(c)Calculate the adiabatic index ? of the gas.(3 marks)
Derive change in internal energy dU in terms of heat capacity at constant volume Cv and change in temperature dT for an deal gas. (3 marks)

QUESTION THREE (20 Marks)
In general, the internal energy is a function of temperature and volume, so that we can write U = U(T,V ). Using this reasoning, show that for a mole of ideal gas. (4 marks)
(b)Calculate the change of entropy
of a bath containing water, initially at 20 ?C, when it is placed in thermal contact with a very large heat reservoir at 80?C. (3 marks)
(ii) of the reservoir when process (i) occurs. The bath and its contents have total heat capacity 104JK-1. (3 marks)
(c) Show that another expression for the entropy per mole of an ideal gas is(3 marks)

(d) If the substance is an ideal monatomic gas, then From this
Calculate
(3 marks)
(e)The work done by a mole of an ideal gas in a reversible adiabatic expansion from can be calculated by determining the area under the PV curve. Show that this work is given by
.
(4 marks)

QUESTION FOUR (20 Marks)
(i) Figure below shows a Carnot cycle. Derive the expression for the heat exhausted
(3 marks)

(ii) For a Carnot Cycle, the ratio of heat input to heat output is equal to the ratio of the highest absolute temperature to the lowest absolute temperature. Show that the work done for the Carnot cycle above is given by (3 marks)

(b) A gasoline engine in a large truck takes in 2500 J of heat and delivers 500 J of mechanical work per cycle. The heat is obtained by burning gasoline with heat of combustion LV =5×104 J/g.
(i) What is the thermal efficiency of this engine? (3 marks)
(ii) How much heat is discarded in each cycle? (3 marks)
(iii) How much gasoline is burned during each cycle? (3 marks)
(iv) If the engine goes through 100 cycles per second, what is its power output in watts? (3 marks)
(v) How much gasoline is burned per second? (2 marks)

QUESTION FIVE (20 Marks)
Using the first law dU = TdS - pdV, derive the four thermodynamic potentials U, H, F, G (in terms of U, S, T, p, V ), and give dU, dH, dF, dG in terms of T, S, p, V and their derivatives.
(4 marks)
Derive all the Maxwell relations.(8 marks)
(c) Given dQ=C_p dT+Adp and dQ=C_V dT+BdVwhere Aand Bare constants
(i) Explain why we can writedQ=C_p dT+Adp anddQ=C_V dT+BdV. (2 marks)
(ii)Show that(C_p-C_V )dT=BdV-Adp(3 marks)
Also show that at constant temperature (?p/?V)_T=B/A(3 marks)

Sph 302 : Thermodynamics question paper

Sph 302 : Thermodynamics Question Paper

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