Chapter 8, Problem 8.44P

Interpretation Introduction

(a)

Interpretation:

Thespecific enthalpy of n-pentane vapor at ${200}^{\circ }\text{C}$ relative to n-pentane liquid at ${20}^{\circ }\text{C}$ is to be determined.

Concept introduction:

According to the Hess’s law, the total enthalpy for a reaction is the sum of all the changes in the multiple steps of the reaction. According to this law, enthalpy is a state function.

Specific heat capacity $\left(C_p\right)$ of a substance is the amount of heat needed for a unit mass of substance to raise its temperature by $1^{\circ }\text{C}$. It is temperature dependent and varies with temperature of the substance. The formula to calculate $C_p$ is:

$C_p\left(T^{\circ }\text{C}\right)=a+bT+c{T}^2+d{T}^3$

(1)

Here, $a,b,c\text{ and }d$ are constants which is specific for a particular substance. The values of these constants are given in table B.2 of appendix B.

Specific enthalpy $\left(\hat{H}\right)$ of any substance at temperature $T^{\circ }\text{C}$ is given by:

$\hat{H}={\int }_{T_{ref}}^T{C}_{p}dT$

(2)

Here, $T_{ref}$ is the reference temperature taken for the calculations.

Interpretation Introduction

(b)

Interpretation:

The specific enthalpy of n-pentane vapor at ${200}^{\circ }\text{C}$ relative to n-pentane liquid at ${20}^{\circ }\text{C}$ is to be determined.

Concept introduction:

The specific enthalpy of any substance at its reference temperature is zero. Also, the change in enthalpy between two states of a substance is the difference between the enthalpies of the two states. Thus,

$\Delta \hat{H}={\hat{H}}_2-{\hat{H}}_1$

(3)

Interpretation Introduction

(c)

Interpretation:

The specific internal energy of the n-pentane vapor at ${200}^{\circ }\text{C and 2}\text{.0 atm}$ is to be determined.

Concept introduction:

For a thermodynamic system, its specific enthalpy $\left(\hat{H}\right)$ is written as:

$\hat{H}=\hat{U}+P\hat{V}$

(4)

Here, $\hat{U}$ is the specific internal energy of the system, $P$ is the pressure of the system and $\hat{V}$ is the specific volume of the system.

The ideal gas law is,

$P\hat{V}=RT$

(5)

Here, $R$ is the universal gas constant with value $8.314\times {10}^{-3}\frac{\text{kJ}}{\text{K}\cdot \text{mol}}$ and $T$ is the temperature of the system.