Serendreamers
Badges: 1
Rep:
?
#1
Report Thread starter 6 years ago
#1
Air at 5 bar, 500K is contained in a cylinder by a piston, and initially occupies a volume of 1m^3. 100kJ of heat are transferred to the air, whilst the volume is kept constant. The temperature in the cylinder after this is 540k. The mass of the air is 3.48kg.

Calculate the pressure in the cylinder at the end of the process.

Using the ideal gas law...

P_2 = \frac {mRT_2}{V} = \frac {3.48 \cdot 287 \cdot 540}{1} = 5.4 \cdot 10^5

Using isentropic relations...

P_2 = P_1 \cdot (\frac {T_2}{T_1})^{\frac {\gamma}{\gamma -1}} = 5 \cdot 10^5 \cdot (\frac {540}{500})^{\frac {1.4}{1.4-1}} = 6.5 \cdot 10^5

Why do I get a different answer? I'm pretty sure that both methods should work..correctly that is
0
reply
username913907
Badges: 10
Rep:
?
#2
Report 6 years ago
#2
(Original post by Serendreamers)
Air at 5 bar, 500K is contained in a cylinder by a piston, and initially occupies a volume of 1m^3. 100kJ of heat are transferred to the air, whilst the volume is kept constant. The temperature in the cylinder after this is 540k. The mass of the air is 3.48kg.

Calculate the pressure in the cylinder at the end of the process.

Using the ideal gas law...

P_2 = \frac {mRT_2}{V} = \frac {3.48 \cdot 287 \cdot 540}{1} = 5.4 \cdot 10^5

Using isentropic relations...

P_2 = P_1 \cdot (\frac {T_2}{T_1})^{\frac {\gamma}{\gamma -1}} = 5 \cdot 10^5 \cdot (\frac {540}{500})^{\frac {1.4}{1.4-1}} = 6.5 \cdot 10^5

Why do I get a different answer? I'm pretty sure that both methods should work..correctly that is
I'm by no means certain but the isetropic derivation probably doesn't involve perfect gases if it gives a different answer.
2
reply
Borek
  • Study Helper
Badges: 4
Rep:
?
#3
Report 6 years ago
#3
Why do you think the process is isentropic?

dS=dQ/T, is dQ zero?
2
reply
QuantumSuicide
Badges: 0
Rep:
?
#4
Report 6 years ago
#4
Wtf? Is this really sixth form stuffs?

Posted from TSR Mobile
2
reply
Serendreamers
Badges: 1
Rep:
?
#5
Report Thread starter 6 years ago
#5
(Original post by Borek)
Why do you think the process is isentropic?

dS=dQ/T, is dQ zero?
Ahh, I'm such a fool. Thank you.

(Original post by QuantumSuicide)
Wtf? Is this really sixth form stuffs?

Posted from TSR Mobile
Nope, that was an accidental mis-labeling. Please forgive me
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Should there be a new university admissions system that ditches predicted grades?

No, I think predicted grades should still be used to make offers (572)
34.35%
Yes, I like the idea of applying to uni after I received my grades (PQA) (684)
41.08%
Yes, I like the idea of receiving offers only after I receive my grades (PQO) (334)
20.06%
I think there is a better option than the ones suggested (let us know in the thread!) (75)
4.5%

Watched Threads

View All