Thermodynamics help on the first law please

[bianca1992]

Hi all I am struggling with this textbook example :( I have applied the formula but the numbers I am getting are really wrong!

A pump compressing hydrogen from a low pressure to a high pressure tank where the tanks pressure is constant and H2 is an ideal gas.
Hydrogen: (H2: MW = 2, Cv = 10 kJ/kgK)
Low pressure tank: (P = 4 bar, T = 30oC)
High pressure tank: (P = 100 bar).

1) Apply the first law of thermodynamics eliminating terms not needed
2) Find the compressor outlet temp when the compression goes along an adiabatic and polytrophic process

 

[bianca1992]

For the first law I have used Q-W = difference in energy and attempted to find the temp via finding the internal energy and enthalpy using deltau = cv x delta T and delta h = cp x delta T where I got 8520 KJ and 12063 KJ but now I am not sure how if I should integrate and remove pressure from the first law and find the temp now.

 

[emailanmol]

Hey,
They are asking you to apply two laws.
Ideal gas law and 1st law.

Clearly till the process is not know you cannot eliminate Q and W from the first law.

Also how did you find value of change in internal energy.(to be precise delta of temperature).

Is the final temp given?

 

[bianca1992]

firstly for the first law does one simply remove pressure from the closed loop first law of thermodynamics?

 

[emailanmol]

I don't understand your question completely.Can you add some more light?

If you want to ask if you can take P out of the integral for calculating work, then it is not allowed unless P is a constant

 

[emailanmol]

From the ideal gas law
PV/T is constant.

So P(1)V(1)/T(1) =P(2)V(2)/T(2)

You know only P(1) P(2) and T (1)
So this won't help.

However, if you know the process like PV^x is constant

Then you can apply ideal gas law and find a relationship between initial amd final volumes and thus initial and final temperature.
(which is how you will solve your 2nd question)

You cannot eliminate any term from the first law for this question as no procesa is stated.You can only substitute relations between variable.
Like you can substitute P with nRT/V

And how did you find delta U and delta H?

 

[bianca1992]

Initially the question is worded quite loosely which is confusing (see top). For the first part of applying the first law of thermodynamics (assuming its a closed system) Q2 = U2 - U1 + 1W2 and this needs to be applied to the system eliminating parts not needed. P cannot be moved as you said

 

[emailanmol]

(re read my previous post.I edited a few parts)

From what I can catch The question is equivalent to stating that an ideal gas H2 is being compressed from State A to B. you have pressure and temp at A and pressure at B.
They want you to find temp at B for a polytropic process which by convention is take as PV^x is constant

Now according to me you cannot eliminate any term from first law.As Q and W are process dependent

Also please amswer how did you find delta U in your 2nd post?

Recheck if you have posted all the data stated in the question

 

[Andrew Mason]

Hi all I am struggling with this textbook example :( I have applied the formula but the numbers I am getting are really wrong!

A pump compressing hydrogen from a low pressure to a high pressure tank where the tanks pressure is constant and H2 is an ideal gas.
Hydrogen: (H2: MW = 2, Cv = 10 kJ/kgK)
Low pressure tank: (P = 4 bar, T = 30oC)
High pressure tank: (P = 100 bar).

1) Apply the first law of thermodynamics eliminating terms not needed
2) Find the compressor outlet temp when the compression goes along an adiabatic and polytrophic process

The compressor takes a volume V_i at P_i and compresses it adiabatically to volume V_f and pressure P_f. P_f=100 and P_i = 4 .

For 1) write out the first law. Since it is adiabatic, what is Q? What does that tell you about ΔU and W?

For 2) apply the adiabatic condition: $PV^\gamma = K$ to find the ratio of initial to final volume. Use the volume and pressure ratios to find the temperature ratio Tf/Ti.

AM

 

[mrajm]

For adiabatic process solve by equation:
w= (Cv+R)(T2-T1)
is this giving correct answer?