Chapter 11, Problem 5SP

(a)

To determine

The Carnot efficiency.

Answer to Problem 5SP

The Carnot efficiency is $44.4\%$.

Explanation of Solution

Given info: The temperature range of the turbine is  $240°\text{C}$ to $650°\text{C}$ and the efficiency is $80\%$.

Write an expression to calculate the efficiency.

$\eta =1-\frac{T_C}{T_H}$

Here,

$\eta$ is the efficiency of the Carnot engine

$T_C$ is the temperature of cold reservoir

$T_H$ is the temperature of hot reservoir

Substitute $240°\text{C}$ for $T_C$ and $650°\text{C}$ for $T_H$ to find $\eta$.

$\begin{array}{c}\eta =1-\frac{\left(240+273\right)\text{K}}{\left(650+273\right)\text{K}}\\ =0.444\\ =\left(0.444\right)\left(100\%\right)\\ =44.4\%\end{array}$

Thus, the Carnot efficiency is $44.4\%$.

Conclusion:

The Carnot efficiency is $44.4\%$.

(b)

To determine

The efficiency of the actual oil-fired turbines.

Answer to Problem 5SP

The efficiency of the actual oil-fired turbines is $35.52\%$.

Explanation of Solution

Write an expression for efficiency of the actual oil-fired turbines.

$\eta \text{'}=80\%\eta$

Here,

$\eta \text{'}$ is the efficiency of the oil-fired power plant.

Substitute $0.444$ for $\eta$ to find $\eta \text{'}$.

$\begin{array}{c}W=\left(80\%\right)\left(0.444\right)\\ =35.52\%\end{array}$

Thus, the efficiency of the actual oil-fired turbines is $35.52\%$.

Conclusion:

Therefore, the efficiency of the actual oil-fired turbines is $35.52\%$.

(c)

To determine

The electrical energy generated by the plant in one hour.

Answer to Problem 5SP

The electrical energy generated by the plant in one hour is $1\times {10}^5\text{kW}\cdot \text{h}$.

Explanation of Solution

Given info: The power of the oil-fired power plant is $100\text{MW}$ and the time is $1\text{h}$.

Write an expression for electrical energy generated by the plant in one hour.

$E=Pt$

Here,

$E$ is the energy

$P$ is the energy

$t$ is the energy

Substitute $100\text{MW}$ for $P$ and $1\text{h}$ for $t$ to find $E$.

$\begin{array}{c}E=\left(100\text{MW}\right)\left(\frac{{10}^3\text{kW}}{1\text{MW}}\right)\left(1\text{h}\right)\\ =1\times {10}^5\text{kW}\cdot \text{h}\end{array}$

Thus, the electrical energy generated by the plant in one hour is $1\times {10}^5\text{kW}\cdot \text{h}$.

Conclusion:

The electrical energy generated by the plant in one hour is $1\times {10}^5\text{kW}\cdot \text{h}$.

(d)

To determine

The heat obtained from oil in each hour.

Answer to Problem 5SP

The heat obtained from oil in each hour is $2.25\times {10}^5\text{kW}\cdot \text{h}$.

Explanation of Solution

Write an expression for efficiency of the actual oil-fired turbines.

$E\text{'}=\frac{E}{\eta \text{'}}$

Here,

$E\text{'}$ is the heat obtained from oil in each hour.

Substitute $0.444$ for $\eta \text{'}$ and $1\times {10}^5\text{kW}\cdot \text{h}$ for $E$ to find $\eta \text{'}$.

$\begin{array}{c}E\text{'}=\frac{1\times {10}^5\text{kW}\cdot \text{h}}{0.444}\\ =2.25\times {10}^5\text{kW}\cdot \text{h}\end{array}$

Thus, the heat obtained from oil in each hour is $2.25\times {10}^5\text{kW}\cdot \text{h}$.

Conclusion:

The heat obtained from oil in each hour is $2.25\times {10}^5\text{kW}\cdot \text{h}$.

(e)

To determine

The amount of oil required to produce $1,700\text{kW}\cdot \text{h}$ in each hour.

Answer to Problem 5SP

The amount of oil required to produce $1,700\text{kW}\cdot \text{h}$ in each hour is $259$ barrels of oil.

Explanation of Solution

Write an expression for the amount of oil required to produce $1,700\text{kW}\cdot \text{h}$ in an hour.

$n=\frac{E\text{'}}{E_h}$

Here,

$E\text{'}$ is the energy released per hour

$E_h$ is the energy released from one barrel oil per hour

$n$ is the  amount of oil required to produce $1700\text{kW}\cdot \text{h}$ in an hour

Substitute $2.25\times {10}^5\text{kW}\cdot \text{h}$ for $E\text{'}$ and $1700\text{kW}\cdot \text{h}$ for $E_h$ to find $n$.

$\begin{array}{c}n=\frac{2.25\times {10}^5\text{kW}\cdot \text{h}}{1,700\text{kW}\cdot \text{h/barrel}}\\ =132.5\text{barrels}\\ \approx \text{133 barrels}\end{array}$

Thus, the amount of oil required to produce $1700\text{kW}\cdot \text{h}$ in each hour is $133$ barrels of oil

Conclusion:

The amount of oil required to produce $1700\text{kW}\cdot \text{h}$ in each hour is $133$ barrels of oil.