Questions: An electrical power station uses 1.33 x 10^14 J of thermal energy input and produces electricity with an efficiency of 37.7%. (a) How much electrical energy is produced? J (b) How much waste energy is produced by the station? HINT: The waste energy is the thermal energy that doesn't result in the production of electricity. J (c) What is the ratio of waste energy to electrical energy output? Please pause for a few seconds to think about whether it's better for this number to be large or small.

An electrical power station uses 1.33 x 10^14 J of thermal energy input and produces electricity with an efficiency of 37.7%.
(a) How much electrical energy is produced?
J
(b) How much waste energy is produced by the station?

HINT: The waste energy is the thermal energy that doesn't result in the production of electricity.
J
(c) What is the ratio of waste energy to electrical energy output?

Please pause for a few seconds to think about whether it's better for this number to be large or small.

Transcript text: (3 Points] DETAILS MY NOTES ASK YOUR TEACHER An electrical power station uses $1.33 \times 10^{14} \mathrm{~J}$ of thermal energy input and produces electricity with an efficiency of $37.7 \%$. (a) How much electrical energy is produced? $\square$ J (b) How much waste energy is produced by the station? HINT: The waste energy is the thermal energy that doesn't result in the production of electricity. $\square$ J (c) What is the ratio of waste energy electrical energy output? \[ \frac{\text { waste energy }}{=} \] $\square$ Please pause for a few seconds to think about whether it's better for this number to be large or small. SUBMIT ANSWER

Solution

Solution Steps

Step 1: Calculate Electrical Energy Produced

The efficiency of the power station is given as $37.7\%$. This means that $37.7\%$ of the thermal energy input is converted into electrical energy.

The thermal energy input is $1.33 \times 10^{14} \, \text{J}$.

The electrical energy produced can be calculated using the formula: \[ \text{Electrical Energy} = \text{Efficiency} \times \text{Thermal Energy Input} \]

Substituting the given values: \[ \text{Electrical Energy} = 0.377 \times 1.33 \times 10^{14} \, \text{J} \]

\[ \text{Electrical Energy} = 5.0141 \times 10^{13} \, \text{J} \]

Final Answer (a)

$\boxed{5.0141 \times 10^{13} \, \text{J}}$

Step 2: Calculate Waste Energy Produced

The waste energy is the thermal energy that does not get converted into electrical energy. This can be calculated by subtracting the electrical energy produced from the total thermal energy input.

\[ \text{Waste Energy} = \text{Thermal Energy Input} - \text{Electrical Energy} \]

Substituting the values: \[ \text{Waste Energy} = 1.33 \times 10^{14} \, \text{J} - 5.0141 \times 10^{13} \, \text{J} \]

\[ \text{Waste Energy} = 8.286 \times 10^{13} \, \text{J} \]

Final Answer (b)

$\boxed{8.286 \times 10^{13} \, \text{J}}$

Step 3: Calculate the Ratio of Waste Energy to Electrical Energy Output

The ratio of waste energy to electrical energy output is given by: \[ \frac{\text{Waste Energy}}{\text{Electrical Energy}} \]

Substituting the values: \[ \frac{8.286 \times 10^{13} \, \text{J}}{5.0141 \times 10^{13} \, \text{J}} = 1.652 \]

Final Answer (c)

$\boxed{1.652}$

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