(i) A 5 m3 outdoor gas storage tank warms from 10°C to 40°C on a sunny day. If t
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Question
(i) A 5 m3 outdoor gas storage tank warms from 10°C to 40°C on a sunny day. If the initial pressure was 0.12 MPa at 10°C, what is the pressure at 40°C, and how many moles of gas are in the tank? Use the ideal gas law.
(ii) (a)What size vessel holds 2 kg water at 80°C such that 70% is vapor? What are the pressure and internal energy?
(b)A 1.6 m3 vessel holds 2 kg water at 0.2 MPa. What are the quality, temperature, and internal energy?
(iii) For water at each of the following states, determine the internal energy and enthalpy using the steam tables.
(iv) Two kg of water exist initially as a vapor and liquid at 90°C in a rigid container of volume 2.42 m3.
(a)At what pressure is the system?
(b)What is the quality of the system?
(c)The temperature of the container is raised to 100°C. What is the quality of the system, and what is the pressure? What are H and U at this point relative to the initial state?
(d)As the temperature is increased, at what temperature and pressure does the container contain only saturated vapor? What is H and U at this point relative to the initial state?
(e)Make a qualitative sketch of parts (a) through (d) on a P-V diagram, showing the phase envelope.
Explanation / Answer
(i) A 5 m3 outdoor gas storage tank warms from 10°C to 40°C on a sunny day. If the initial pressure was 0.12 MPa at 10°C, what is the pressure at 40°C, and how many moles of gas are in the tank? Use the ideal gas law.
Apply Ideal Gas Law
V = 5 m3 = 5000 L
P1 = 0.12 MPa, P2 = X
T1 = 10C = 283K T2 = 40C = 313 K
a)
First, let us calculate moles
PV = nRT
P = 0.12 MPa = 0.12*10^6 Pa
n = PV/(RT) = ( 0.12*10^6 )(5)/(8.314*283)
n = 255.008 moles
Now,
Calculate P2:
PV = nRT
P(5) = 255.008*8.314*(313)
P = 255.008*8.314*(313)/5 = 132,720.54565 Pa = 0.132 MPa
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