Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
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Chapter 5, Problem 54P

a)

To determine

The change in enthalpy (Δh) during heating process.

a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The initial temperature (T1) is 600 K.

The final temperature (T2) is 1000 K.

Calculation:

Refer the table A-2, ”Ideal gas specific heats of various common gases table”,

 Obtain the following constant values.

  a=28.90b=0.1571×102c=0.8081×105d=2.873×109

Write the mean change in enthalpy (Δh¯) for an ideal gas during heating process from state 1 to state 2.

  Δh¯=12c¯p(T)dT        (I)

Here, mean specific heat at constant volume function of temperature is c¯v(T) and change in temperature is dT.

Substitute a+bT+cT2+dT3 for c¯v(T) in Equation (I).

  Δh¯=12[a+bT+cT2+dT3]dT        (II)

Here, constant is a, b, c and d.

Integrate the Equation (II).

  Δh¯={a(T2T1)+12b(T22T12)+13c(T23T13)+14d(T24T14)}        (III)

Substitute T2=1000K, T1=600K, and constants (a, b, c, and d) in Equation (III).

  Δh¯={(28.90)(1,000K600K)+12(0.1571×102)((1,000K)2(600K)2)+13(0.8081×105)((1,000K)3(600K)3)+14(2.873×109)((1,000K)4(600K)4)}=12,544kJ/kmol

Refer table A-1, “Molar mass properties table”,

The molar mass of nitrogen substance e (M) as 28.013kg/kmol.

Write the change in enthalpy (Δh) during heating process.

  Δh=Δh¯M

  Δh=12,544kJ/kmol28.013kg/kmol=447.8kJ/kg

Thus, the change in enthalpy (Δh) during heating process is 447.8kJ/kg.

b)

To determine

The change in enthalpy (Δh) at temperature of 500 K.

b)

Expert Solution
Check Mark

Explanation of Solution

Refer the table A-2, ”Ideal gas specific heats of various common gases table”, obtain the specific heat at constant pressure of nitrogen gas at temperature of 800 K as 1.121kJ/kgK.

  cp,avg=1.121kJ/kgK

Write the change in enthalpy (Δh) at a temperature of 500 K.

  Δh=cp,avg(T2T1)

  Δh=(1.121kJ/kgK)(1,000K600K)=448.4kJ/kg

Thus, the change in enthalpy (Δh) at temperature of 500 K is 448.4kJ/kg.

c)

To determine

The change in enthalpy (Δh) at room temperature.

c)

Expert Solution
Check Mark

Explanation of Solution

Refer the table A-2, ”Ideal gas specific heats of various common gases table”, obtain the specific heat at constant volume of nitrogen gas at temperature of 300 K as 1.039kJ/kgK.

  cp,avg=1.039kJ/kgK

Write the change in enthalpy (Δh) at room temperature.

  Δh=cp,avg(T2T1)

  Δh=(1.039kJ/kgK)(1,000K600K)=415.6kJ/kg

Thus, the change in enthalpy (Δh) at room temperature is 415.6kJ/kg.

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Chapter 5 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

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