Prove that µi = (∂U/∂ni)S,V,nj = (∂H/∂ni)S,P,nj = (∂A/∂ni)T,V,nj
6. We have said that U = U(T,V) and H-H(T,P). However, it is possible to write U- U(T,P). If this is the casc, then Note carefully the change in variables Show that for any system av
1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the differentiable vector function u and real-valued function f, prove: lu(f(t)))= f(t)u' (f (t))
1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the differentiable vector function u and real-valued function f, prove: lu(f(t)))= f(t)u' (f (t))
1· Let S {u,v) be a linearly, independent set. Prove that(u+ v.u-v) is linearly independent. 2. Let H :2y1. Prove that H is not a subspace of f2.
s)If each of the following counts as an "item" A G S H U P T V Cv πΤ α-Kr μ do a derivation to express the following partial derivative only in terms of 2 or less items au
s)If each of the following counts as an "item" A G S H U P T V Cv πΤ α-Kr μ do a derivation to express the following partial derivative only in terms of 2 or less items au
thermodynamic
The enthapy H(s, P, N) idefine as the Legeandre transform the intern eneryy u (s, v N) wit respect to the volume v e enina Using swular analogy discussed earlier for Helmh。Ita function develsp equations for T,V and Silar ana
The enthapy H(s, P, N) idefine as the Legeandre transform the intern eneryy u (s, v N) wit respect to the volume v e enina Using swular analogy discussed earlier for Helmh。Ita function develsp equations for T,V and Silar...
Q4
(b) Prove that ker P = ker Tn ker S. () h a Question 4. Define T: Ma2 = c+ d. Prove that T is a linear transformation R by T C and onto. Find dim(ker T). Is T one-to-one? Jamomials in P. Show
(b) Prove that ker P = ker Tn ker S. () h a Question 4. Define T: Ma2 = c+ d. Prove that T is a linear transformation R by T C and onto. Find...
Problem 6. Let V, W, and U be finite-dimensional vector spaces, and let T : V → W and S : W → U be linear transformations (a) Prove that if B-(Un . . . , v. . . . ,6) is a basis of V such that Bo-(Un .. . ,%) s a basis of ker(T) then (T(Fk+), , T(n)) is a basis of im(T) (b) Prove that if (w!, . . . ,u-, υ, . . . ,i)...
thermodynamic
The enthapy H(s, P, N) idefine as the Legeandre transform the intern eneryy u (s, v N) wit respect to the volume v e enina Using swular analogy discussed earlier for Helmh。Ita function develsp equations for T,V and Silar ana
Boiler P=8000 kPa, T =73°C U=305 H=306 kJ/kg P=8 MPa, T=400°C U=2867 H=3142 kJ/kg S = 6.37 kJ/kg.K) W pump Pump Qboller Turbine Wurm Condenser Sat. liq., P=30 kPa U=289 H=290 kJ/kg P = 30 kPa, x = 0.90, U'= 289 H'= 290 UY= 2467 H'=2625 kJ/kg s'=0944 s'= 7.77 kJ/kg.K) Qcondenser For the steam power plant shown above, if the mass flow rate of the steam is 10 kg/s and the surrounding temperature is 25°C, determine the following: a....
3. Let U be a subspace of R", and let p :R" Rº be the projection v H proju v. Prove that a) p is a linear operator b) im T = U and ker T = U1 c) dim U + dim Ut = n.