A spherical tank is being designed to hold 10 moles of carbon dioxide gas at an absolute pressure of 5 bar and a temperature of
1 answer:
Answer:
r=0.228m
Explanation:
The equation that defines the states of a gas according to its thermodynamic properties is given by the general equation of ideal gases
PV=nRT
where
P=pressure =5bar=500.000Pa
V=volume
n=moles=10
R = universal constant for ideal gases = 8.31J / (K.mol)
T=temperature=80F=299.8K
solvig For V
V=(nRT)/P
we know that the volume of a sphere is
solving for r
solving
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Answer:
Explanation:
According to the first thermodynamic law, the energy must be conserved so:
Where Q is the heat transmitted to the system, U is the internal energy and W is the work done by the system.
This equation can be solved by integration between an initial and a final state:
(1)
As per work definition:
For pressure the force F equials the pressure multiplied by the area of the piston, and considering dx as the displacement:
Here A*dx equals the differential volume of the piston, and considering that any increment in volume is a work done by the system, the sign is negative, so:
So the third integral in equation (1) is:
Considering the gas as ideal, the pressure can be calculated as , so:
In this particular case as the systems is closed and the temperature constant, n, R and T are constants:
Replacion this and solving equation (1) between state 1 and 2:
The internal energy depends only on the temperature of the gas, so there is no internal energy change , so the heat exchanged to the system equals the work done by the system: