Show steps please Oxygen (O2) at 450 K is heated to 850 K. Assume oxygen as an i

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Oxygen (O2) at 450 K is heated to 850 K. Assume oxygen as an ideal gas. Determine the change in internal energy and enthalpy of oxygen per unit mass, using: data for u and h from the Oxygen table (Method 1), average specific heat values (Method 2). Answers: (a) Delta u = 302.0 kJ /kg, Deltah = 406.0 kJ /kg, Deltam = 303.2 kJ I kg, Deltah = 406.8 kJ/kg. A 10-kg metal block initially at 200 degree C and 1 MPa is heated to 500 degree C and 100 MPa. The metal block has a density of 2000 kg/m3 and a specific heat of 2 kJ/kg.K. Calculate the change in the total internal energy and total enthalpy of the metal block. Assume the metal block as an incompressible substance and its specific heat as constant. Answers: DeltaU = 6000 kJ, DeltaH = 6495 kJ. H4-3: 100-kg of R-134a at 200 kPa is contained in a piston-cylinder device whose volume is 12.322 m3.The piston is now moved until the volume is one-half its original size. This is done such that the pressure of the R-134a does not change. Determine the change in the total internal energy of the R-134a. Answers: DeltaU = -11.0 MJ. H4-4: Nitrogen flows steadily through a pipe with a constant cross-section area of 6 cm2. The nitrogen enters the pipe at 500 kPa and 50 degree C with a velocity of 15 m/s. The nitrogen leaves the pipe at 200 kPa and 25 degree C. Assume that the nitrogen behaves as an ideal gas. Determine the density, volume flow rate, and mass flow rate of nitrogen at the inlet; Determine the density and volume flow rate of nitrogen at the exit. Answers: rho1 =5.21 kg/m3, V1 = 0.009 m3/s, m1 = 0.0469kg/s. rho2 = 2.26 kg/m2, V2 = 0.0208 m3/s.

Explanation / Answer

H4-1:

Ideal gas properties of oxygen give

a. At 450 K

h1 = 13228 kJ/kmol

u1 = 9487 kJ/kmol

At 850 K

h2 = 26218 kJ/kmol

u2 = 19150 kJ/kmol

1 kmol of O2 = 32 kg of O2

du = u2 - u1 = 19150 - 9487 = 9663 kJ/kmol = 9663/32 = 301.97 kJ/kg

dh = h2 - h1 = 26218 - 13228 = 12990 kJ/kmol = 12990/32 = 405.94 kJ/kg

b. Using specific heat

At 450 K

Cp = 0.956 kJ/kg-K

Cv = 0.696 kJ/kg-K

At 850 K

Cp = 1.064 kJ/kg-K

Cv = 0.804 kJ/kg-K

Average Cp = (0.956+1.064)/2 = 1.01 kJ/kg-K

Average Cv = (0.804+0.696)/2 = 0.75 kJ/kg-K

du = Cv(T2 - T1) = 0.75*400 = 300 kJ/kg

dh = Cp(T2 - T1) = 1.01*400 = 404 kJ/kg

H4-2: Since the metal block is an incompressible substance, its density is constant, hence volume is constant.

Change in internal energy, dU = mC(T2-T1)

C = 2 kJ/kg-K

m = 10 kg

T2 - T1 = 500 - 200 = 300 K

dU = 10*2*300 = 6000 kJ

Enthalpy = H = U + pV

p = pressure

V = Volume

Volume of block = 10/2000 = 0.005 m3

Change in enthalpy, dH = dU + Vdp (Since V is constant)

dp = 100 - 1 = 99 MPa = 99000 kPa

dH = 6000 + 0.005*99000

dH = 6000 + 495 dH = 6495 kJ

H4-3:

http://www.ohio.edu/mechanical/thermo/property_tables/R134a/R134a_PresSat.html

http://www.ohio.edu/mechanical/thermo/property_tables/R134a/R134a_Super1.html

Specific Volume of r134a before piston moves v1 = 12.322/100 = 0.12322 m3/kg

Specific Volume of r134a after piston moves v2 = v1/2 = 0.12322/2 = 0.06161 m3/kg

At 200 kPa v1>vg, so it is a superheated vapor

Enthalpy, h1 = 287.7 kJ/kg

vf<v2<vg, so it is saturated

v2 = vf + x*vfg 0.06161 = 0.0007534 + x*(0.00991466)

x = 0.61

Enthalpy, h2 = hf + x*hfg h2 = 164.94 kJ/kg

Change in enthalpy, dH = 100(164.94 - 287.7) = -12275.63 kJ

dH = dU + pdV

dH - pdV = dU

-12275.63 - 200*(6.161 - 12.322) = dU

dU = -11043.43 kJ dU = -11.043 MJ

H4-4:

http://yeroc.us/calculators/gas-density.php

Using above site

Density of N2 at inlet

d1 = 5.213 kg/m3

Volumetric Flow rate, v1 = velocity*cross section area = 15*6/10000 = 0.009 m3/s

Mass flow rate, m = d1*v1 = 0.009*5.213 = 0.0469 kg/s

Density at outlet

d2 = 2.26 kg/m3

Since mass flow rate is constant for ideal gas flow

Volumetric flow rate

v2 = m/d2 = 0.0469/2.26 = 0.0208 m3/s

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