Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

PHY 3513: Thermodynamics Midterm Examination Solutions, Exams of Thermal Physics

University of Florida (UF)Thermal Physics

Material Type: Exam; Class: THERMAL PHYSICS; Subject: PHYSICS; University: University of Florida; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 09/17/2009

koofers-user-njr
koofers-user-njr 🇺🇸

3.5

(2)

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
February 11, 2005 Name: -----------------------------.
PHY 3513:Kumar
I Midterm Examination: Solutions
1) A tank of volume 1.0 m3 contains oxygen at a pressure of 1.5×106 Pa and a
temperature of 20° C. Assume that oxygen behaves like an ideal diatomic gas.
a) How many kilomoles of oxygen are in the tank?
n=P1V1 /RT = 1.5
×
106
×
1/(8.314
×
103
×
293) = 0.616 kilomoles
b) How many kilograms?
m=n
×
32kg/kilomoles = 19.7kg
c) Find the pressure if the temperature is raised to 500° C.
P2=(P1/T1)
×
T2 = (773/293)
×
1.5
×
106 = 3.96
×
106Pa
d) At 20°C, how many kilomoles can be withdrawn form the tank before the
pressure falls to 10% of the original pressure.
Δ
n = 0.9PV/RT = 0.9
×
1.5
×
106
×
1/8.314
×
103
×
293 = 0.554 kilomoles
2) Show that for a van der Waals’ gas β/κ = R/(v-b).
Here please note that
β
/
κ
= dP/dT|v = R/(v-b).
3) In the cycle shown, P1 = 10 atm, V1 = 2 m3 , V2 = 4 m3 and n= 1 kilomole. The gas is
diatomic and the step 1Æ 2 is adiabatic.
i) What is T2?
ii) How much work does this engine do?
iii) What is the efficiency of this engine?
The parameters of the system are: T1 = P1 V1 /nR =
10
×
1.013
×
105
×
2/8.314
×
103=243.69K
Also P2 = P1(V1/V2)
γ
=10.13
×
105/21.4=3.84
×
105Pa; T3 = P2V1/nR = 92.34K.
1. Since 1
Æ
2 is adiabatic and the gas is diatomic (
γ
= 1.4), T2=(V1/V2)0.4 T1 =
184.68K
2. Qh=ncv(T1-T3) = (5/2)8.314
×
103(243.69-92.34) = 3.15
×
106 J
|Qc|=ncp(T2-T3) = (7/2)8.314
×
103(184.68-92.34) = 2.69
×
106 J
W = Qh-Qc = 0.46
×
106 J.
3.
η
= W/Qh = 0.146
⇒
14.6%.
1
2
P
V
pf2

Partial preview of the text

Download PHY 3513: Thermodynamics Midterm Examination Solutions and more Exams Thermal Physics in PDF only on Docsity!

February 11, 2005 Name: -----------------------------.

PHY 3513:Kumar

I Midterm Examination: Solutions

  1. A tank of volume 1.0 m^3 contains oxygen at a pressure of 1.5× 106 Pa and a temperature of 20° C. Assume that oxygen behaves like an ideal diatomic gas.

a) How many kilomoles of oxygen are in the tank?

n=P 1 V 1 /RT = 1.5 × 106 ×1/(8.314 × 103 ×293) = 0.616 kilomoles

b) How many kilograms?

m=n ×32kg/kilomoles = 19.7kg

c) Find the pressure if the temperature is raised to 500° C.

P 2 =(P 1 /T 1 ) ×T 2 = (773/293) ×1.5× 106 = 3.96 × 106 Pa

d) At 20°C, how many kilomoles can be withdrawn form the tank before the pressure falls to 10% of the original pressure.

Δn = 0.9PV/RT = 0.9 ×1.5× 106 ×1/8.314 × 103 ×293 = 0.554 kilomoles

  1. Show that for a van der Waals’ gas β/κ = R/(v-b).

Here please note that β/ κ = dP/dT| v = R/(v-b).

  1. In the cycle shown, P 1 = 10 atm, V 1 = 2 m^3 , V 2 = 4 m^3 and n= 1 kilomole. The gas is diatomic and the step 1Æ 2 is adiabatic.

i) What is T 2? ii) How much work does this engine do? iii) What is the efficiency of this engine?

The parameters of the system are: T 1 = P 1 V 1 /nR =

10 ×1.013× 105 ×2/8.314 × 103 =243.69K

Also P 2 = P 1 (V 1 /V 2 )^ γ^ =10.13 × 105 /21.4=3.84 × 105 Pa; T 3 = P 2 V 1 /nR = 92.34K.

1. Since 1 Æ2 is adiabatic and the gas is diatomic ( γ = 1.4), T 2 =(V 1 /V 2 )0.4^ T 1 =

184.68K

2. Qh =nc v(T 1 -T 3 ) = (5/2)8.314 × 103 (243.69-92.34) = 3.15 × 106 J

|Qc|=nc p (T 2 -T 3 ) = (7/2)8.314 × 103 (184.68-92.34) = 2.69 × 106 J

W = Qh -Qc = 0.46 × 106 J.

3. η = W/Qh = 0.146 ⇒ 14.6%.

P

V

  1. Forty kg of water at 0°C must be frozen into ice in a refrigerator. The room temperature is 25° C. The latent heat of fusion of water is 3.33× 105 J/kg. What is the minimum power required if the freezing has to occur in an hour?

Minimum power must come from the most efficient refrigerator, which is a Carnot cycle. The coefficient of performance of a Carnot refrigerator is c = Qc/W = Tc/(Th - Tc ).

Therefore the power 3600

= × ×

= (^) c c

h cQ T

T T

P =339W.