If gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form P = ((nRT)/(V-nb))-((an^2)/(V^2)), in which a, b, n, and R are constants. Find dP/dV.

Question

anonymous · Answer

nRT/(v-nb)^2+an^2/2V^3    i belive let me double check

anonymous · Answer

Okay... can you show me your work?

anonymous · Answer

well furnctions in the form of 1/(x-g) have a derivative -1/(x-g)^2 and functions of the form 1/x^2 have a derivative -1/2x^2 and these are in this form as a,b,n,R are constants

anonymous · Answer

so the first term would be negative

anonymous · Answer

sorry    -1/2x^3 my mistake

anonymous · Answer

again a mistake haha sorry -2/v^3

anonymous · Answer

Sorry, I'm kind of lost. I understand that because a, b, n, R are constants, then their derivative is 0 right? Then I don't understand what to do...

anonymous · Answer

there derivative is zero but your differentiating with respect to V so just treat the constants as numbers and then differentiate accordingly.

anonymous · Answer

$$d(nRT/(V-nb))dV=-nRT/(V-nb)^2$$

anonymous · Answer

and $$d(-an^2/V^2)dV=2an^2/V^3$$

anonymous · Answer

Then wouldn't the answer be 1? |dw:1315987596445:dw|