# Homework Help: Tough Thermodynamics mass flow Problem Help!

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1. Apr 23, 2015

### SweetDReynolds

1. The problem statement, all variables and given/known data

Problem: In order to simplify your analysis, you will assume alcohol has the same properties of water so you can use the steam tables. You load the 30 gallon still 1/3 full with nearby water at 1 bar and 20°C and mash(assume the mash has negligible influence on properties and total mass in comparison to water to simplify your analysis). You wish to achieve an alcohol volumetric flow rate out of the still at 10 gal/hr with the alcohol leaving as a saturated vapor at 80°C.
a) What is the total mass in the still?
b)What is the mass flow rate of alcohol [gm/hr] leaving the still and the time it takes to completely empty the still in [hr] (assuming all water and mash will leave the still as alcohol)?
c) How much heat in [kJ] and entropy generation in [kJ/kg] occurs over the still emptying process given a constant furnace temperature of 1000°F.

V=Volume, v=specific volume, V_flow=volumetric flow, Q=heat transfer

Attempt:
Known: T_1=20°C, Q=10 gal/hr, V_1=(1/3)30 gal = 10 gal

Took state 1 as the liquid and state 2 as the alcohol vapor inside the still...

2. Relevant equations
Conservation of mass, conservation of energy, conservation of entropy
∆m_cv+m_i-m_e=0
m=V/v(dt)
mdot=(Velocity*A/v)
Q(volumetric flow)=AV
The change in mass within the control volume+sum of the massflows entering-sum of the mass flows exiting=0
∆E_cv=1Q2-1W2+Σmdot_i(h_i)-Σmdot_e(h_e)
simplifies to m_2*u*2-m_1*u*1=1Q2-mdot_e?

3. The attempt at a solution
a) m_total=m_1+m_2? unless there is no mass at state 2..
m_1=V/v
v(20 C)=.0010016 m^3/kg
m_1 = 10gal/.0010016 m^3/kg = 37.7936 kg

b) Conservation of mass equation (a is the nomenclature denoted at the outlet on the diagram)
m_2-m_1=-mdot_a
m_a=(Vel_a*A/v_a)dt or V_a/v_a
V_flow=Vel_a*A
v_a(80 C)=.0010291m^3/kg

From here i would integrate my mass flow over time and do m_a(t2-t1) and take t1 to be 0.

c) -Q_1/2=m_1*u_1-m_2*u_2-mdot_a*h_a

really, i do not know what state 2 is, do i need it in my analysis?

Could just be an analysis error/using wrong simplifications of the equations. Need mass flow to move forward with problem.

Any direction would be appreciated. Thank you!

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2. Apr 23, 2015

### Staff: Mentor

If the still has 10 gallons to begin with, and it is emptied at 10 gph, how much is left after 1 hour? How much exited during that 1 hour? What mass exited during the 1 hour?

Chet