Homework 1

The Energy Quality (Exergy to Energy ratio) of Radiative Energy is X/E=1-4TO/3T-1/3(TO/T)^4 ,A particular space heater operates at 800C [Exergy is defined with respect to the environment - T0 = 298 or 300 K, room temperature a. Calculate the energy quality for this space heater.

1-((4*293)/(3*1703))+.3(293/1073)^4=.638

Calculate the energy quality for the space heater used in space (background radiation temperature of 2.7 K

6 points, -2 for neglecting K to ºC conversion 1-((4*2.7)/(3*1703))+.3(2.7/1073)^4=.997

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1910

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The Exergy Flow diagram (Figure 6.5) shows that while 0.18 TW of exergy is used for Lighting, only 0.012 TW of this is converted to visible radiation. a. Describe at least one factor that contribute to the loss of exergy, considering the types of light sources/bulbs available.

Exergy Loss Factors (1+ factors; 3 points) • Exergy lost as heat • Incandescent Lamp produces excess IR radiation due to reduced operating temperature relative to Sun

What are two major differences between Energy and Exergy? Illustrate one of these differences with an example

Exergy is not conserved, but Energy is conserved. Exergy is the fraction of Energy available for work, but not all Energy can be recovered as work. Exergy must be defined with respect to the environment

Calculation of Utilized Solar Fraction

Figure 6.5 shows that 0.0017 TW of Solar Electricity were generated in 2009. The total Exergy Flows for Solar Energy sources are 900 TW and 162,000 TW, respectively. To calculate the Utilized Solar Fraction: Utilized Solar Fraction = 0.0017 TW / 162,000 TW = 0.000000105 or 1.05 x 10^-8 Therefore, the fraction of Solar Energy that is recovered from the total Exergy Flows of these sources is approximately 1.05 x 10^-8.

. Assuming a linear growth rate in solar use from 2009 to 2050 and that we will increase total energy use from 18 to 30 TW in 2050, what percentage of global energy use would solar account for in 2050

Growth Rate (2 points) - 6,647% increase from 2009 to 2021 à 6647 % / 12 years = 553.9 %/year Further Increase (2 points) - 29 years, 553.9% per year - 29 x 553.9% = 16060 % Increase from 2009 Total Value in 2050 (3 points) - 16060% x 0.0017 TW = 16060/100 x 0.0017 TW = 0.273 TW in 2050 Percentage of Total Energy Use (2 points) - 0.273 TW / 30 TW = 0.0091 = 0.91 %

Which type of light source would be most helpful in reducing the wasted exergy?

In order of increasing Efficiency (Select LED or fluorescent; 3 points) • Incandescent < halogen lamp << fluorescent < LED

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Find a recent estimate of solar energy generation today, citing your source and converting units as needed. What percentage has it increased since 2009?

Recent Estimate (5 points) - 994 TWh of Solar PV Energy in 2021,Note that we need to convert to TW! 1 TW over the course of a year = 8760 TWh [8760 h = 365 days x 24 hrs/day] Hence, 994 TWh = 0.113 TW [-3 points if the units are not in TW and are not converted accordingly] Percentage Increase (5 points) - 0.113 TW / 0.0017 TW *100 = 6,647% Increase

Which biofuel source is more energetically viable, corn-based or sugarcane-based ethanol?

Sugarcane ethanol is more energetically viable because substantially more energy can be obtained than what is put in to grow it, whereas corn-based ethanol offers less energy.

: What is the energy output-to-input ratio of corn-based ethanol? How does it compare to that of sugarcane-based ethanol?

The energy output-to-input ratio of corn-based ethanol is around 1.3, whereas that of sugarcane-based ethanol is between 8.3 and 10.2.

Assume that a wise guy has taken the name too seriously and brought their space heater to space to keep them warm. If the operating temperature remains the same, will the energy quality increase or decrease?

The energy quality will increase because T0 is reduced, lowering the subtractive term. This can also be rationalized non-numerically by realizing that lowering T0 increases the temperature difference, so according to the laws of thermodynamics, the process should be more efficient.

What impact does the difference in energy output-to-input ratio have on the economic viability of corn-based and sugarcane-based ethanol?

The extra energy in sugarcane-based ethanol increases the cost of corn-based ethanol beyond the cost of sugarcane ethanol, lowering the economic viability of corn-based ethanol.

What policy has the US government enacted due to the difference in energy output-to-input ratio between corn-based and sugarcane-based ethanol?

The increased costs have led the US government to add taxes and tariffs to sugarcane ethanol, motivating the use of US farm-grown corn for biofuel and protecting the domestic industry.

The sign of the formula changes - this is because the hot and cold temperatures effectively switch. Why then does the energy quality remain positive? Relate this to the capacity to do work.

The temperatures are switched, so the direction of thermal energy flows would reverse. However, this temperature difference can still be harnessed to do work (in this case cooling), hence liquid helium is a remarkably powerful refrigerant. This is due to the environmental conditions we choose - if the exergy was considered relative to absolute zero or the temperature of space, then the energy quality would be vastly lower. While the low energy of the helium at these temperatures reflects the work done in liquifying it, this work is not stored as energy. Instead, it contributes to add exergy by increasing the temperature difference as compared with the environment. Thus, exergy increases while energy decreases, contributing to a high energy quality.

Re-read Box 3.2 and Figure 3.6. According to the US Energy Information Administration, the US electric power sector generated 1,440 million metric tons of CO2 emissions in 2020. How does this compare with the lowest and highest potential values estimated for 2030 in Figure 3.6 - are we trending in the right direction?

The value is near the lowest potential values (range roughly 1,000 to 2,200 million metric tons). (3 points) This means that we are hitting many of the targets specified in that report - We are trending in the right direction. (3 points)

Find a recent estimate of per capita energy use in Dallas, Texas, or the US. Cite your source and convert the value to both Joules and kilowatt-hours. Do you think your personal energy use is higher or lower than this value? Why?

Value and Source (2 points) 79,897 KWh in US Conversion (2 point) 79,897 KWh x 3.6 x 106 J/KWh = 2.88 x 1011 J Personal energy use is lower (2 points) - industrial manufacturing and other uses are accounted for in a per-capita measurement, so my personal consumption is likely lower than this value.

Liquid Helium-4 has a boiling point of 4.2 K at atmospheric pressure. a. Calculate the energy quality of liquid helium, considering only the thermal energy of the system. Take the absolute value if needed.

X/E=1-To/T=(1-293/4.2)=68.8

1850

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