How much heat is added to the gas when it is compressed suddenly?

AI Thread Summary
The discussion revolves around calculating the heat added to gas during sudden compression. The initial work done on the gas is calculated as 2 Joules, while the work associated with pressure change is estimated at 1.05E-3 Joules. Participants clarify that the question focuses on heat addition rather than work done, emphasizing that any energy not converted to work contributes to the internal energy of the gas, thus increasing its temperature. There is no heat flow from the surroundings, leading to the conclusion that all energy from the work done contributes to the gas's internal energy. Ultimately, the total energy added to the gas is considered to be approximately 2 Joules.
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Homework Statement



http://imgur.com/44ay2.png"
44ay2.png


Homework Equations



Below.

The Attempt at a Solution



A.
W=Fd 2000N x 0.001m = 2J

B.
This is where I am stuck. Can I assume that the pressure doesn't change when it is pushed in because it says that it is pushed in "suddenly"?
If so then I get: W = \int p \cdot dV = p(V_f - V_i) 105Pa x (0.01m^2 x 0.001m) = 1.05E-3 J

C
Is this just the difference between the two above i.e. 2 - 1.05E-3 = 1.99895J?

I get the feeling this is wrong since I didn't use the information that its 1 litre and 300K anywhere here...
 
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a) The system consists of the cylinder of air and the piston. So the work done on the system is 2000 N x .001 m = 2 Joules, as you found. Note: if the piston had mass, this would not be the work done on the gas. This is because the piston gains kinetic energy so some of the added energy would go into the piston rather than the gas. But since the piston is massless, this is ignored.

b) The question does not ask how much work has been done on the gas. It asks how much heat has been added to the gas. Has there been any heat flow from the surroundings into the gas (to the instant before the piston is stopped)?

c) Is there is any heat flow out of the gas? So where does all the energy go? (use the first law).

AM
 
Thanks for the reply.
Andrew Mason said:
b) The question does not ask how much work has been done on the gas. It asks how much heat has been added to the gas. Has there been any heat flow from the surroundings into the gas (to the instant before the piston is stopped)?
None from the surrounding, but my reasoning is that of the work done by pushing the piston, some will go into compressing the gas and the rest will go to internal energy and therefore increase the temperature. So actually the answer would be 2 - 1.05E-3 = 1.99895J ?
Andrew Mason said:
c) Is there is any heat flow out of the gas? So where does all the energy go? (use the first law).
Nope. So it's just the total amount - ie. 2J?
 

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