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(CENG131)[2008](s)hw2~jcychan^_10024.pdf
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CENG131
CHEMICAL ENG GINEERING THERMODYN NAMICS
HONG KONG UNIVERSSITY OF SCIENCE AND TECHNOLOGY,SPRING G 2009
HOMEWORK #2
PROBLEM
Your first job as an astronautic en ngineer is to tackle a technical problem with a sma all jet used for altitude adjustment in space on ou ur new lunar landing pod. These jets are powered d by low-pressure nitrogen gas, stored in a 0.4-m3, w well-insulated spherical tank at 1 bar pressure. To operate the jets, nitrogen must flow out of the tank k at a constant rate of 7 g/s. Since the pressure ins side the tank must always be kept at 1 bar, a he eater will be used to heat up the remaining nitroge en in the tank as time goes on. Initially, the tempera rature inside the tank is 280 K. Assume that nitrog gen has a constant heat capacity, CP= 29.1 Jm mol-1K-1.
(a).Express the instantaneous s temperature T as a function of time, t, and the fo ollowing constants: (the initial n number of moles of nitrogen in the tank), (the m molar flow rate), and (the initial temperaature).
(b)You need to specify how to o control the heating power supplied by the heate er to maintain the required operating conditiions. Provide an expression for the instantaneous s rate of heat flow, . , as a function time, , t, and known constants.
(c).If, for safety reason, the temmperature
of the tank cannot be higheer than
1000 K, how long can we o operate the
jets? What is the total amo ount of heat
required for that period off time?
(d)Upon receiving your analy ysis, your
boss thought that your con nstant heat
capacity assumption migh ht
significantly underestimat te the total
amount of heat required. Re Redo your
calculation using the CP vallues from
Table C.1 of your textbook k.
SOLUTION
SYSTEM
We will choose the content of the nitrogen tank as our system. It is a control-vo olume, open system, with diathermal, rigid d and permeable boundaries.
We define two different states s: at the initial conditions, before the flow starts (s subscript 0), and at time t (no subscript).
SYMBOL DEFINITIONS AND GIVENN INFORMATION
11K-1
R = gas constant = 8.314 Jmol-
= Pressure of system (const tant throughout at 1 bar)
= Molar mass of nitrogen gaas = 28 g mol-1
. = Mass flow rate of nitrogen n (constant throughout at 7 g/s)
= The constant-volume hea at capacity of nitrogen
= The constant-pressure he eat capacity of nitrogen = 29.1 Jmol-1K-1
=
Number of moles of nitrog gen in the system at time t
. = Molar rate of accumulationon of nitrogen in the system
=
Temperature of the system m at time t
.. = 280 K
= Total volume of the system m = 0.4 m3
= Molar volume of the system m at time t
= Instantaneous heat rate in nto system at time t
= Total heat transferred tto system from the beginning until time t
GOALS
Express (a) the instantaneous temperature of the system, T, and (b) the instant taneous heat rate
as a function of time. Calcul