Thermo question - final mass/entropy generation

In summary, 1) A tank is filled with air at a temperature of 20 degrees Celsius.2) entropy is generated during the cooling of the tank. 3) The final mass of air in the tank is 1.51 kg.
  • #1
goblue88888
5
0
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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  • #2
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.
 
  • #3
chemisttree said:
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.

Thanks chemisttree for your response!
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.
 
  • #4
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.
 

1. What is the final mass in a thermo question?

The final mass in a thermo question refers to the total mass of a system after a given process or reaction has occurred. It can be calculated by taking into account the initial mass, any mass added or removed during the process, and any changes in density.

2. How is entropy generation calculated in a thermo question?

Entropy generation is calculated by taking into account the heat transfer and temperature changes in a system. It is typically measured in joules per kelvin (J/K) and can be calculated using the equation S_gen = Q/T, where Q is the heat transfer and T is the temperature in Kelvin.

3. What is the significance of final mass and entropy generation in thermodynamics?

The final mass and entropy generation are important quantities in thermodynamics as they help to understand and analyze the changes that occur in a system during a process or reaction. These values can provide insight into the efficiency and sustainability of a system, as well as the potential for energy production.

4. How do changes in mass and entropy affect the overall energy balance of a system?

Changes in mass and entropy can greatly impact the energy balance of a system. Mass changes can result in changes in the amount of energy required or released during a process, while entropy changes can affect the direction and efficiency of energy transfer within the system.

5. Are there any limitations to using the final mass and entropy generation in thermodynamics?

While the final mass and entropy generation are important quantities in thermodynamics, there are some limitations to their use. These values are only applicable to closed systems, where there is no mass or energy transfer with the surroundings. Additionally, they may not accurately represent real-world systems due to the simplifications and assumptions made in thermodynamics calculations.

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