Question

A gas in a cylinder has its state changed according to the law, P(V^1.2) = C, where P is pressure, V is volume, and C is a constant. Initially, P_1 = 16 kN/m^2, and V_1 = 0.78 m^3.

From the given law P(V^1.2) = C, find an expression for dP/dV.

Answer 1

Find C first :)

Answer 2

Substitute P_1 and V_1 to the equation to find C :)

Answer 3

C is equal to 11.87499.

Answer 4

Express the formula in terms of P :)

Answer 5

P = 11.875 / (V^1.2)

Answer 6

Then differentiate it.

Answer 7

But wouldn't it become 0?

Since a constant's derivative is equal to 0.

Answer 8

Nope, because it's a constant divided by a variable's exponent.

Answer 9

Try to make the variable in the numerator :)

Answer 10

(The index will be negative)

Answer 11

11.875V^(-1.2), you mean?

Answer 12

Yep, then you know what to do?

Answer 13

Let me try it...

Answer 14

Mm... I got -14.25/(V^2.2), but the answer key states -14250/(V^2.2).

I'm not sure where the 1000 went.

Answer 15

The 1000 is hidden in the unit kN ;)

Answer 16

Wait, is it because my P_1 is in kN?

Answer 17

Yep exactly :D

Answer 18

Aha, then I understand. Thank you very much!

Answer 19

No problem :D