Heat exchanged in Expanding and cooling gas

In summary, the conversation discusses a solution to a problem involving the first law of thermodynamics. The original solution gives a positive value for the amount of heat exchanged, while the textbook solution gives a negative value. It is determined that the textbook solution is incorrect and the original solution is correct.
  • #1
ChiralSuperfields
1,305
138
Homework Statement
Please see below
Relevant Equations
Please see below
For part(b),
1680335521558.png

My solution is,
##\Delta E_{int} = Q - W = \frac{3}{2}(P_fV_f - P_iV_i)##
##Q = W + \frac{3}{2}(P_fV_f - P_iV_i)##
##Q = 4000 + \frac{3}{2}((1 \times 10^6)(6 \times 10^{-3}) - (3 \times 10^6)(2 \times 10^{-3})##
##Q = 4000 J##

However, according to the solution b. ##−4000 J##

Can someone please tell me what I did wrong?

Many thanks!
 

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  • #2
I'm uncertain what would in general be meant by the amount of heat "exchanged" by a system. It could mean the amount gained, the amount lost, or the magnitude of the transfer (so positive). Looks like they intended the amount lost.
 
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  • #3
Your answer is correct.
 
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  • #4
haruspex said:
I'm uncertain what would in general be meant by the amount of heat "exchanged" by a system. It could mean the amount gained, the amount lost, or the magnitude of the transfer (so positive). Looks like they intended the amount lost.
Thank you for your reply @haruspex!

If they intended for the amount lost, why dose the first law in my answer give the wrong sign? If you don't know, please don't worry about it, this textbook dose have a lot of mistakes!

Many thanks!
 
  • #5
Chestermiller said:
Your answer is correct.
Thank you for your reply @Chestermiller ! That is reassuring. Do you please know whether the reason I am correct is because the textbook solution is wrong?
 
  • #6
ChiralSuperfields said:
Thank you for your reply @Chestermiller ! That is reassuring. Do you please know whether the reason I am correct is because the textbook solution is wrong?
Obviously
 
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  • #7
Chestermiller said:
Obviously
Thank you for your help @Chestermiller !
 

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