# If P=nRT / V  where n, R and T are constants, what is  dP / dV ?  Select the correct answer from the following:-If P=nRT / V  where n, R and T are constants, what is  dP / dV ?  Select the...

If P=nRT / V  where n, R and T are constants, what is  dP / dV ?  Select the correct answer from the following:-

If P=nRT / V  where n, R and T are constants, what is  dP / dV ?  Select the correct answer from the following:-

dP/dV = - nRT/V

dP/dV = 2 nRT/V^2

dP/dV = nRTV

dP/dV = nRT/V

dP/dV =  -nRTV

dP/dV =  -nRT/V^2

dP/dV = -2 nrt/V2

dP/dV = nRT/V^2

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to differentiate the function P with respect to V, considering n,R,T as constants such that:

`(dP)/(dV) = (nRT)(d(1/V))/(dV)`

You need to differentiate the function `1/V`  with respect to V, using the quotient rule, such that:

`(d(1/V))/(dV) = (((d(1))/(dV))*V - 1*(dV)/(dV))/(V^2)`

`(d(1/V))/(dV) = (0*V - 1*1)/(V^2)`

`(d(1/V))/(dV) = -1/(V^2)`

Substituting -`1/(V^2)`  for `(d(1/V))/(dV)`  yields:

`(dP)/(dV) = (nRT)(-1/(V^2))`

`(dP)/(dV) = -(nRT)/(V^2)`

Hence, differentiating P with respect to V, under given conditions, yields `(dP)/(dV) = -(nRT)/(V^2),`  thus, you should select the sixth option from the given list.

Sources:

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The value of P is given as `P=(nRT)/V`   where n, R and T are constants.

`(dP)/(dV) = -1*n*R*T*V^-2`

=> `-(n*R*T)/V^2`

Of the given choices `(dP)/(dV) = -(n*R*T)/V^2`