Question

by direct differentiation of h = u pv, obtain a relation between (δh/δu)p and (δu/δv)p. this is mainly a math problem similar to one already given

Answer 1

To obtain a relation between (δh/δu)p and (δu/δv)p using direct differentiation, differentiate the given equation h = u pv with respect to u and v while keeping p constant.

Step-by-step explanation:

To obtain a relation between (δh/δu)p and (δu/δv)p using direct differentiation, let's start by differentiating the given equation h = u pv with respect to u while keeping p constant:

1. Differentiate each term of h = u pv with respect to u:

(δh/δu)p = v + u(p/p)

1. Next, differentiate the equation h = u pv with respect to v while keeping p constant:

(δh/δv)p = up

So, the relation is:

(δh/δu)p = v + u(p/p)

(δh/δv)p = up