Chapter 1, Problem 15P

To determine

The constant-pressure specific heat of air at $25°\text{C}$ in $\text{kJ}/\text{kg}\cdot \text{K}$, $\text{J}/\text{g}°\text{C}$, $\text{kcal}/\text{kg}\cdot °\text{C}$ and $\text{Btu}/\text{lbm}\cdot °\text{F}$.

Explanation of Solution

Write the expression of conversion relation for the constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{kJ}/\text{kg}\cdot \text{K}$.

  $\begin{array}{c}{c}_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)=c_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)\times \frac{1\text{kJ}/\text{kg}\cdot \text{K}}{1\text{kJ}/\text{kg}\cdot °\text{C}}\\ =c_p\left(\text{kJ}/\text{kg}\cdot \text{K}\right)\end{array}$

Convert the unit of constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{kJ}/\text{kg}\cdot \text{K}$ at $25°\text{C}$ using the above relation.

  $\begin{array}{c}{c}_p=1.005\text{kJ}/\text{kg}\cdot °\text{C}\\ =1.005\text{kJ}/\text{kg}\cdot °\text{C}\times \frac{1\text{kJ}/\text{kg}\cdot °\text{C}}{1\text{kJ}/\text{kg}\cdot \text{K}}\\ =1.005\text{kJ}/\text{kg}\cdot \text{K}\end{array}$.

Thus, the constant-pressure specific heat of air at $25°\text{C}$ in $\text{kJ}/\text{kg}\cdot \text{K}$ is $1.005\text{kJ}/\text{kg}\cdot \text{K}$.

Write the expression of conversion relation for the constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{J}/\text{g}°\text{C}$ using the above relation.

  $\begin{array}{c}{c}_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)=c_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)\times \frac{1000\text{J}}{1\text{kJ}}\times \frac{1\text{kg}}{1000\text{g}}\\ =c_p\left(\text{J}/\text{g}°\text{C}\right)\end{array}$

Convert the unit of constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{J}/\text{g}°\text{C}$ at $25°\text{C}$.

  $\begin{array}{c}{c}_p=1.005\text{kJ}/\text{kg}\cdot °\text{C}\\ =1.005\text{kJ}/\text{kg}\cdot °\text{C}\times \frac{1000\text{J}}{1\text{kJ}}\times \frac{1\text{kg}}{1000\text{g}}\\ =1.005\text{J}/\text{g}°\text{C}\end{array}$

Thus, the constant-pressure specific heat of air at $25°\text{C}$ in $\text{J}/\text{g}°\text{C}$ is $1.005\text{J}/\text{g}°\text{C}$.

Write the expression of conversion relation for the constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{kcal}/\text{kg}\cdot °\text{C}$ using the above relation.

  $\begin{array}{c}{c}_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)=c_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)\times \frac{1\text{kcal}}{4.1868\text{kJ}}\\ =c_p\left(\text{kcal}/\text{kg}\cdot °\text{C}\right)\end{array}$

Convert the unit of constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{kcal}/\text{kg}\cdot °\text{C}$ at $25°\text{C}$ using the above relation.

  $\begin{array}{c}{c}_p=1.005\text{kJ}/\text{kg}\cdot °\text{C}\\ =1.005\text{kJ}/\text{kg}\cdot °\text{C}\times \frac{1\text{kcal}}{4.1868\text{kJ}}\\ =0.240\text{kcal}/\text{kg}\cdot °\text{C}\end{array}$

Thus, the constant-pressure specific heat of air at $25°\text{C}$ in $\text{kcal}/\text{kg}\cdot °\text{C}$ is $0.240\text{kcal}/\text{kg}\cdot °\text{C}$.

Write the expression of conversion relation for the constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{Btu}/\text{lbm}\cdot °\text{F}$ using the above relation.

  $\begin{array}{c}{c}_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)=c_p\left(\text{kJ}/\text{kg}\cdot °\text{C}\right)\times \frac{1\text{Btu}/\text{lbm}\cdot °\text{F}}{4.1868\text{kJ}/\text{kg}\cdot °\text{C}}\\ =c_p\left(\text{Btu}/\text{lbm}\cdot °\text{F}\right)\end{array}$

Convert the unit of constant-pressure specific heat of air from $\text{kJ}/\text{kg}\cdot °\text{C}$ to $\text{Btu}/\text{lbm}\cdot °\text{F}$ at $25°\text{C}$ using the above relation.

  $\begin{array}{c}{c}_p=1.005\text{kJ}/\text{kg}\cdot °\text{C}\\ =1.005\text{kJ}/\text{kg}\cdot °\text{C}\times \frac{1\text{Btu}/\text{lbm}\cdot °\text{F}}{4.1868\text{kJ}/\text{kg}\cdot °\text{C}}\\ =0.240\text{Btu}/\text{lbm}\cdot °\text{F}\end{array}$

Thus, the constant-pressure specific heat of air at $25°\text{C}$ in $\text{Btu}/\text{lbm}\cdot °\text{F}$ is $0.240\text{Btu}/\text{lbm}\cdot °\text{F}$.