A heater is used to heat 100 SCM of nitrogen in a rigid vessel from 26.85oC to...

A heater is used to heat 100 SCM of nitrogen in a rigid vessel from 26.85^oC to 126.85^oC. Do energy balance and calculate heat duty Q (kJ) using data from Table A-2a,b,c and A18. State your assumption and explain your results.

Solutions

Expert Solution

Heat volumetric flow V = 100 SCM

SCM - standard cubic meter

At Standard condition 1 mol having 22.4 L or

1kmol having volume of ideal gas = 22.4 m3

1 m3 having = 1/22.4 kmol

100 m3 having = 100/22.4 kmol = 4.464 kmol

Nitrogen moles n= 4.464 kmol

T1 = 26.85 C = 273 +26.85 = 299.85 K

T2 = 126.85 C = 273 + 126.85 = 399.85 K

Specific heat of Nitrogen,

Cp(kj/kmol.k) = a + bT + cT^2 + dT^3

By table,

a = 28.90

b = -0.1571 *10^-2

c = -0.8081*10^-5

d = -2.8713*10^-9

Change in enthalpy ,

dH = nCpdT

dH = n(a + bT + cT^2 + dT^3)dT

Integrate both sides, from temperature T1 to T2

ΔH = n[ a(T2 - T1) + b/2 * (T2^2 - T1^2) + c/3 * (T2^3 - T1^3) + d/4 * (T2^4 - T1^4)

ΔH = 4.464 kmol*[ 28.90*(399.85 - 299.85) - 0.1571*10^-2/2 *(399.85^2 - 299.85^2) - 0.8081*10^-5/3 *(399.85^3 -299.85^3) - 2.8713*10^-9/4 *(399.85^4 - 299.85^4)]

ΔH =4.464*( 2890 -54.96 -99.58-12.546)

ΔH = 12155 kJ

Heat required for heating in this case,

Q = ΔH = 12155 kJ

Amanda K answered 1 week ago

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