Differentiation: Given lnP= -X/RT + c,where X and R are constant..Compute dlnp/dT

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to differentiate both sides such that:

`d(lnP)= (-X/RT)dT + c`

Notice that you need to differentiate the right side with respect to T, considering X,R and c as constants such that:

`d(lnP) = (-(X/R)*(T^(-1)) + c)(dT)`

`d(lnP) = ((-(X/R)*(-T^(-2)) + 0)dT`

You need to divide both sides by `dT`  such that:

`(d(lnP))/(dT) = (X/R)*(1/(T^2))`

`(d(lnP))/(dT) = X/(RT^2)`

Hence, evaluating `(d(lnP))/(dT)`  under given conditions yields `(d(lnP))/(dT) = X/(RT^2).`

jeew-m eNotes educator| Certified Educator

lnP = -X/(RT)+c

if c is a constant

d(lnP)/dT = -(X/R)d(1/T)/dT+d(c)/dT

              = -(X/R)(-1/T^2)+0

              = X/(RT^2)


so d(lnP)/dT =  X/(RT^2)