Gas expansion/compression?

[collegelife101]

Hello everyone,

This might be a stupid question, but I'm having some difficulty understanding gas compression and expansion such as with this question:

Two gases, each 1 L at STP, are allowed to spontaneously react in an insulated cylinder with a floating piston to form 2 new gaseous products such that total moles are constant before and after the reaction. Immediately after the completion of the reaction the volume of the cylinder was measured to be 1.82 L, therefore the reaction was endothermic.

In the solution, it says that because the volume went down the temperature went down, making this an endothermic reaction. I guess I just don't see how the temperature can decrease when the volume decreases, as temperature should increase when a gas is compressed? Does it depend on if the reaction is endothermic and exothermic?

Also, for an adiabatic process, how do we know that deltaU= -w?

Thank you!

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[medic86]

For the first question:

PV = nRT

STP: 0 C, 1 atm
n = moles held constant
R = gas constant
P = 1 atm (derived from STP)

V before reaction: 1 L + 1 L = 2 L
V after reaction: 1.82 L
Therefore, volume decreased after the reaction.

solve for V:

V = nRT/P

For V to decrease, with n, R, and P essentially being constant, the temperature must have decreased.




For the second question, I can't recall.

 

[lexw]

adiabatic = no change in internal energy.

E = q - w

0 = q - w

q = -w

 

[blackmi4]

No.

Adiabatic means heat doesn't flow into or out of the system. it means q=0.

dU=q-w

q=0

dU=-w

http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Thermal/ImportantThermalProcess.html

 

[lexw]

ops! yeah your completely right! sorry was confusing it with isothermal and my math was completely wrong -_-

 

[collegelife101]

How do you know that the pressure is constant here? Thanks!

For the first question:

PV = nRT

STP: 0 C, 1 atm
n = moles held constant
R = gas constant
P = 1 atm (derived from STP)

V before reaction: 1 L + 1 L = 2 L
V after reaction: 1.82 L
Therefore, volume decreased after the reaction.

solve for V:

V = nRT/P

For V to decrease, with n, R, and P essentially being constant, the temperature must have decreased.




For the second question, I can't recall.

 

[medic86]

How do you know that the pressure is constant here? Thanks!

The reaction is carried-out at STP, standard temperature and pressure. Standard pressure is 1 atm.

 

[collegelife101]

Thank you again! I'm sorry if this is a stupid question, but are we just to assume that the pressure stays constant? I'm just thinking that because there is a change in volume, there could also be a change in pressure.

The reaction is carried-out at STP, standard temperature and pressure. Standard pressure is 1 atm.