ABSTRACT
Problem 2. If z = f (u,v,w) and z =3u2 −2v +4w3v2 find the total differential, dz
The total differential
dz = ∂z ∂u
du + ∂z ∂v
dv + ∂z ∂w
dw
∂z
∂u = 6u (i.e. v and w are kept constant)
∂z
∂v = −2 + 8w3v
(i.e. u and w are kept constant) ∂z
∂w = 12w2v2 (i.e. u and v are kept constant)
Hence
dz=6udu + (8vw3 − 2) dv + (12v2w2)dw
Problem 3. The pressure p, volume V and temperature T of a gas are related by pV =kT , where k is a constant. Determine the total differentials (a) dp and (b) dT in terms of p, V and T .
