2h2o
Oct9-11, 12:48 AM
1. The problem statement, all variables and given/known data
A compressor takes 90 kg/min of helium at 120 kPa and 310 K and compresses it to
700 kPa and 430K. A heat loss of 20 kJ/kg of helium flowing is noted.
Determine:
(a) the work required by the compressor (kJ/kg), and
(b) the power required to drive the air compressor (kW).
Assume helium is an Ideal Gas; M = 4 kg/kmol; Cp = 5/2R.
2. Relevant equations
PLEASE SEE ATTACHED PHOTO FOR MY WORK AND ATTEMPT.
3. The attempt at a solution
The solutions are given as
(a) 643.6 kJ/kg
(b) +965.4 kW
My questions are:
a) I would not have realized that this 643.6 kJ/kg result was actually what was asked (work req'd by compressor) had the solution not been given. This was just an intermediate result to what I thought I was working towards. So how would I know that "the work req'd by compressor" is actually asking for this? And what symbol would this be denoted by?
Work (W) has SI units of J = Nm = kgm^2/s^2. So it's not W... but what? The phrasing of the question has me confused.
b) According my Mass Energy balance expression of the 1st LoTh; with cancellations and strategic assumptions, Wdot= mdot(deltah) -Qdot.
So to calculate Wdot, I have a unit mismatch unless I bring Qdot inside the parenthetical expression. But multiplying Qdot by mdot is nowhere in my relation of the 1st Law. This seems like magic--and bad mathematics--to me. But it yields the correct (given) solution. Some insight here would be helpful.
Thanks!
JC
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
A compressor takes 90 kg/min of helium at 120 kPa and 310 K and compresses it to
700 kPa and 430K. A heat loss of 20 kJ/kg of helium flowing is noted.
Determine:
(a) the work required by the compressor (kJ/kg), and
(b) the power required to drive the air compressor (kW).
Assume helium is an Ideal Gas; M = 4 kg/kmol; Cp = 5/2R.
2. Relevant equations
PLEASE SEE ATTACHED PHOTO FOR MY WORK AND ATTEMPT.
3. The attempt at a solution
The solutions are given as
(a) 643.6 kJ/kg
(b) +965.4 kW
My questions are:
a) I would not have realized that this 643.6 kJ/kg result was actually what was asked (work req'd by compressor) had the solution not been given. This was just an intermediate result to what I thought I was working towards. So how would I know that "the work req'd by compressor" is actually asking for this? And what symbol would this be denoted by?
Work (W) has SI units of J = Nm = kgm^2/s^2. So it's not W... but what? The phrasing of the question has me confused.
b) According my Mass Energy balance expression of the 1st LoTh; with cancellations and strategic assumptions, Wdot= mdot(deltah) -Qdot.
So to calculate Wdot, I have a unit mismatch unless I bring Qdot inside the parenthetical expression. But multiplying Qdot by mdot is nowhere in my relation of the 1st Law. This seems like magic--and bad mathematics--to me. But it yields the correct (given) solution. Some insight here would be helpful.
Thanks!
JC
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution