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### Topic: Thermodynamics - First Law Problem  (Read 1907 times)

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#### YuliaSnow

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##### Thermodynamics - First Law Problem
« on: September 25, 2016, 07:08:45 PM »
I have been trying to figure out how to do this problem for a few hours, hoping someone can help me out.

Question:

An air mattress (of volume 50L) is inflated using a solid called  "A" with a molar mass of 10g/mol. "A" decomposes and produces "B", a gas at a ratio of 1:1.5. Each mole of A also produces an enthalpy of ΔH=-10kJ. Assume 70% of this energy is deposited in "B" and decomposition is instantaneous. Also let "B" be an ideal gas with Cp,m=30J/mol/K. In order for the mattress to work properly, it should reach a pressure of 3 atm when fully inflated.

a) Estimate the mass in g of "A" needed to use the air mattress. State any assumptions or approximations being made.
Hint: Treat the decomposition of "A" and the expansion of "B" as two separate processes.

b) Find the temperature of "B" after the mattress is fully inflated.
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Here is my attempt at it:

I assumed the temperature is at room temp (298K) and pressure is starting at 1 atm.

I used q=(10kJ/mol*1000J/kJ*30%*2/3*n) since 70% was put in "B".
Some equations I used:
PV=nRT
dU=CvdT for ideal gas
Cv=Cp-nR

U=q+w
dU=CvdT=dq+PdV
Integrate
(nCp,m-nR)(T2-T1)=(10kJ/mol*1000J/kJ*30%*2/3*n)+0
T2=(10kJ/mol*1000J/kJ*30%*2/3)/(Cp,m-R)+T1=390K

n=PV/RT=(3atm)(50L)/(0.082057Latm/mol/K)/390K=4.687mol

massA=(MA)(1/1.5)*nB
=31.2g
T2=390K