# Thermo question - final mass/entropy generation!

I think I may have posted this in the wrong forum earlier :\

## Homework Statement

An insulated and initially empty 0.7m^3 tank is connected by a valve to a line flowing air at 50degreesC and 200kPa. The valve is opened until the tank is filled, and then the valve is closed. The insulation is then removed from the tank, and a 20degreeC heat sink cools the tank until the air inside reaches a temperature of 30degreesC. 1) What is the final mass of air in the tank? 2) How much entropy is generated during the cooling of the tank?

## Homework Equations

1)
PV=mRT
2)
S2-S1=Cp*ln(T2/T1)-R*ln(P2/P1)
m(s2-s1)=Integral(dQ/T)+S-gen

## The Attempt at a Solution

1) I tried figuring out the final temperature, and since V and R are constant, I got P2=P1*T2/T1=200kPa*303K/323K=187.62kPa. I then used this P to get m=PV/RT. So m=(187.62*0.7)/(0.287*323)=1.417kg.. Is this right?
2) Using the first equation, I get 1.004*ln(303/323)-0.287*ln(187.62/200)=-0.0458.. But this is wrong right since it shouldn't be negative?
Then I try putting it into the second equation, 1.417*-0.0458 - Integral(dQ/303)=S-gen.. but I don't know how to do the Integral and dQ part... any help? THANKS!!

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chemisttree
Homework Helper
Gold Member
Write out your units for the gas constant... you have 0.287 for the value (its wrong).
In 1), you are using the pressure you calculated at the final temperature, P2. What temperature are you using in your calculation, T1 or T2?

You can't do 2) until you figure out what value to use as the gas constant.

Write out your units for the gas constant... you have 0.287 for the value (its wrong).
In 1), you are using the pressure you calculated at the final temperature, P2. What temperature are you using in your calculation, T1 or T2?

You can't do 2) until you figure out what value to use as the gas constant.
For 1).. I accidentally put in T1! Oops!
P2 = P1*T2/T1 = 200kPa*303K/323K = 187.62kPa
So it should be (187.62kPa*0.7m^3)/(0.287kJ/kg-K*303K) = 1.51kg.
However.. isn't 0.287kJ/kg-K correct since it's the R for air? :\ Not R-bar or anything else.

chemisttree
Homework Helper
Gold Member
What is 'm' in PV=mRT? Is it mass? Should it be 'n' or moles? Did you do a calculation like n=m/M where m is mass of air and M is molar mass of air?

In the equation

S2-S1 = Cp*ln(T2/T1) - R*ln(P2/P1), what units did you use for Cp? Value is 1.004. It seems to me that the units should be the same as that for R since you are performing a subtraction.

Look at your units for the calculation that yields 1.51 kg. Just write down the units and you get an answer that will be in units of KPa m^3 kg K/kJ K.
Is a kJ equal to KPa*m^3?

I would suggest writing out all of the equations you intend to use and identify the units that you will use. Tabulate your known information in a table that expresses the information in the units you have identified. Substitute into the equations you are given and solve.