Thermal & Kinetic Lecture 22

Problems Class II

Thermal & Kinetic paper, ’04/’05: Q1

Is it possible for the temperature of an ideal gas to rise without heat flowing into the gas?

Yes N

o

Don’t

know

0% 0%0%

1. Yes

2. No

3. Don’t know

Must the temperature of an ideal gas necessarily change as a result of hear flow into or out of it?

Yes N

o

Don’t

know

0% 0%0%

1. Yes

2. No

3. Don’t know

Thermal & Kinetic paper, ’02/’03: Paper 2, Q2

…compare to CW Set 4

Q1. 1 mole of an ideal gas originally at a pressure of 1.0 x 104 Pa and occupying a volume of 0.2 m3 undergoes the following cyclic process:

(i) an adiabatic compression until the pressure is 3.0 x 104 Pa;(ii) an isobaric expansion to a volume of 0.4 m3;(iii) an isothermal expansion until the pressure reaches 1.0 x 104 Pa;(iv) an isobaric compression to the original volume of 0.2 m3.

Draw a PV diagram for this process [3].

For each of the stages (i) – (iv) calculate the heat transferred [5], the work done [5], and the change in internal energy [5].

Show that only internal energy is a function of state [2].

V (m3)

P (kPa)

A

B C

D

30

10

0.2 0.4 V (m3)

P (kPa)

A

B C

D

30

10

0.2 0.4

F31ST1 CW4

Stage 1 Stage2 Stage 3 Stage 4 Total

Work done +1.5 kJ -9 kJ -13.175 kJ + 10 kJ -10.675 kJ

Heat transferred

0 22.5 kJ 13.175 kJ -25 kJ +10.675 kJ

Change in internal energy

+1.5 kJ +13.5 kJ 0 -15 kJ 0

Thermal & Kinetic paper, ’06/’07: Q7

What do you need to use to solve this type of PV cycle question?

• Ideal gas law: PV = nRT• First law: U = Q + W• Equation for adiabatic, P1V1

P2V2

• Equation for adiabatic work:• Q = CvT (isochoric); • Q = CPT (isobaric)• Work done in isothermal, isobaric, isochoric

process• Only internal energy is a function of state

11122

VPVP

Numerical answers to all (past!) exam questions are on web at:

http://www.nottingham.ac.uk/physics/intranet/undergrad/ug_numericalanswers.php

Q5. F31ST1 ’03 – ’04 Exam Paper

What is the net change in internal energy of the gas for one cycle of the engine?

0 J

90

J

180

J 6

0 J

Don’t

know

93%

0% 3%3%0%

a) 0 J

b) 90 J

c) 180 J

d) 60 J

e) Don’t know

When moving from point A to point B, what is the change in the volume of the gas?

90

m3

2 m

3

45

m3

32

m3

Don’t

know

11%

54%

21%

0%

14%

a) 90 m3

b) 2 m3

c) 45 m3

d) 32 m3

e) Don’t know

Q3. F31ST1 ’06 – ’07 Exam Paper

Dimensions of Boltzmann’s constant?

M2L

2 T2

Q

M2L

2 T2

Q-1

M2L

T-1

Q-1

ML2

T-2Q-1

Don’t

know

0%6%

13%

75%

6%

a) M2L2 T2b) M2L2 T2

c) M2L T-1

d) ML2 T-2

e) Don’t know

If the energy levels are spaced by 0.25 eV and the number of molecules with energy E1 is a factor of 10-5

smaller than the number with energy E0, calculate the value of T.

101

K

211

2 K

273

K

252

K

None

of the

se

Don’t

know

0% 0%

26%

5%

63%

5%

a) 101 K

b) 2112 K

c) 273 K

d) 252 K

e) None of these

f) Don’t know

Q2. F31ST1 ’04 – ’05 Exam Paper

How many ways are there of distributing the energy?

618

0 1021

12

Don’t

know

24%

4% 4%4%

64%a) 6

b) 180

c) 10

d) 2112

e) Don’t know

What is the probability of finding the system in a state where each oscillator has one quantum of energy?

50% 8% 10

% 1%

Don’t

know

0%6% 6%

0%

88%a) 50%

b) 8%

c) 10%

d) 1%

e) Don’t know

Q8(b). F31ST1 ’05 – ’06 Exam Paper

Total energy of configuration B?

e

2e

4e

5e

Don‘t

know

0% 0% 0%0%0%

a) b) 2c) 4d) 5e) Don‘t know

Q8(b). F31ST1 ’05 – ’06 Exam Paper

What is the equilbrium temperature of the system?

100

C 5

0 C

Nei

ther

of t

hese

Don’t

know

0% 0%0%0%

a) 100 C

b) 50 C

c) Neither of these

d) Don’t know

Will the total change in entropy be:

Posi

tive

Neg

ativ

e Z

ero

Don’t

know

0% 0%0%0%

a) Positive

b) Negative

c) Zero

d) Don’t know