# 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*

### 2 Answers | Add Yours

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:**

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`