# Heat exchanged in Expanding and cooling gas

• ChiralSuperfields
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.
ChiralSuperfields
Homework Statement
Relevant Equations
For part(b),

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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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.

ChiralSuperfields

ChiralSuperfields
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.

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!

Chestermiller 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?

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

ChiralSuperfields
Chestermiller said:
Obviously
Thank you for your help @Chestermiller !

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