How Is Work Calculated When Compressing Gas?

AI Thread Summary
The discussion focuses on calculating work and internal energy changes during gas compression at constant pressure. The work done on the gas is determined using the formula W = P(Vf - Vi), resulting in a negative value since the gas is compressed. The internal energy change is calculated using the equation U = Q + W, where Q represents heat lost. Clarification is provided that positive work indicates expansion, while negative work indicates compression. Understanding these concepts is crucial for accurately solving the problem.
Negan57
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Homework Statement



Pt. A) A gas is compressed at a constant pressure of 0.632 atm from 7.11 L to 5 L. In the process,
440 J of energy leaves the gas by heat.
What is the work done on the gas?
Answer in units of J

Pt. B)

What is the change in its internal energy?
Answer in units of J

Homework Equations



PV = nRT
U = Q + W
1 atm = 101325 pa
1L = .001m^3

The Attempt at a Solution


A)

.632atm = 64037.4 pa
7.22L = .00711 m^3
5L = .005 m^3

W = P(Vf -Vi)
=
64037.4(.005-.00711)
=
-135.189

U = Q+W

U = -135.189 -440
=
-575.1189

OR (done other ways)
: 304.881
: -304.881
: 575.118914

All of these were wrong. Please help?

B) ...
 
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Negan57 said:

The Attempt at a Solution


A)

.632atm = 64037.4 pa
7.22L = .00711 m^3
5L = .005 m^3

W = P(Vf -Vi)
Is this the work done ON the gas or the work done BY the gas? What does the question ask for?
B) ...
What is W in U = Q + W? (ie is it work done ON or BY the gas?).

AM
 
It asks for the work done ON the gas. The reasons its W = P(Vf-Vi) and not W = -P(Vf-Vi) is because its work ON gas not BY the gas. In U = Q + W, W is work on gas presumably, though I'm not 100% sure.
 
Negan57 said:
It asks for the work done ON the gas. The reasons its W = P(Vf-Vi) and not W = -P(Vf-Vi) is because its work ON gas not BY the gas. In U = Q + W, W is work on gas presumably, though I'm not 100% sure.
This is important. Positive work is done BY the gas when it expands. The work done BY the gas is PΔV where ΔV>0. Positive work is done ON the gas when it is compressed. So the work done ON the gas is -PΔV.

So, in the expression U = Q+W, the W is work done ___ the gas.(hint: if W is positive is there an expansion or compression?).

AM
 
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