Question

Find the work done on the ideal gas:

Answer 1

Relation:

Answer 2

Work done = area under the curve from A to B

Answer 3

Yes, correct.

Answer 4

Area of the segment + area of rectangle ?

Answer 5

correct

Answer 6

Now area of segment ?

I remember that area of segment = Area of sector - area of triangle. but not quite sure how to apply this here.

Answer 7

ah, I see. so you're not necessarily sure if it is a semicircle they've made.

Answer 8

Not semi-circle as

Radius y-axis = (500-300) * 10^3 = 2*10^5 Pa
Radius x-axis = (6-3.6) * 10^-3 = 2.4 * 10^-3 m^3

Answer 9

I know what you're saying, but they're completely different units anyway.

Answer 10

and I doubt we can turn Pa into m^3

Answer 11

to get a dimensionally correct answer\[\frac{1}2\pi \left(\frac{V_2 - V_1}2\right)\left(\frac{P_2 - P_1}2\right) \]apply the above

Answer 12

V2 = 6 , V1 = 3.6 or V1 = 1.2

Answer 13

If you see what I did, I just wrote the radius in two different ways as the formula is \(1/2 \pi r \times r\)

Answer 14

r = (V2-V1)/2 = Diameter/2

Answer 15

But how did you induce that ?

Answer 16

Just to get a dimensionally correct answer. That's all. Try getting an answer this way.

Answer 17

2193.6 correct.

Answer 18

Oh did you get that answer?

Answer 19

Used your formula and compared it to the book final answer which is 2194

Answer 20

Good :)

Answer 21

Thanks !