Heat exchanged in Expanding and cooling gas

[member 731016]

Homework Statement

Please see below

Relevant Equations

Please see below

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!

 

[haruspex]

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.

 

[Chestermiller]

Your answer is correct.

 

[member 731016]

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!

 

[member 731016]

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?

 

[Chestermiller]

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

 

[member 731016]

Obviously

Thank you for your help @Chestermiller !