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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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).`

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

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)

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