Exam 17: Energy Conservation

A house has $155 \mathrm {~m} ^ { 2 } \text { of exterior walls consisting of } 2.9 \mathrm {~cm} \text { of exterior }$ wood, $15 \mathrm {~cm}$ of insulation, and $2.0 \mathrm {~cm}$ of interior wood. (a) On a winter day when the interior temperature is $20 ^ { \circ } \mathrm { C }$ and the exterior temperature is $- 2 ^ { \circ } \mathrm { C }$ , what is the daily heat loss through the walls if they are insulated with fiberglass wool? (b) What is the percent reduction in heat loss if the fiberglass wool is replaced with polystyrene foam sheets?

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Question 1

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(a) The power loss is given by
$P = A \Delta T / R$ The total $R$ -value is given by the sum of the values for the exterior wall, the insulation and the interior wall as
$R = R _ { e x t } + R _ { i n s } + R _ { i n t }$
where $R$ is defined as
$R = l / k$
Using SI units the thermal conductivity of wood is $k = 13 ( \mathrm {~W} \cdot \mathrm { cm } ) / \left( \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } \right)$ . For fibreglass wool $k = 3.8 ( \mathrm {~W} \cdot \mathrm { cm } ) / \left( \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } \right)$ . So for walls with fibreglass wool the total $R$ -value will be
$R = \frac { 2.9 \mathrm {~cm} } { 13 \frac { \mathrm { W } \cdot \mathrm { cm } } { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } } + \frac { 15 \mathrm {~cm} } { 3.8 \frac { \mathrm { W } \cdot \mathrm { cm } } { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } } + \frac { 2.0 \mathrm {~cm} } { 13 \frac { \mathrm { W } \cdot \mathrm { cm } } { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } } = 4.32 \frac { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } { \mathrm { W } }$
The power loss is given by
$P = \left( 155 \mathrm {~m} ^ { 2 } \right) \times \left( 20 ^ { \circ } \mathrm { C } + 2 ^ { \circ } \mathrm { C } \right) / \left[ 4.32 \left( \mathrm {~m} ^ { 2 } { } ^ { \circ } \mathrm { C } \right) / \mathrm { W } \right] = 789 \mathrm {~W}$
(b) If polystyrene foam is used with a thermal conductivity $k = 2.84 ( \mathrm {~W} \cdot \mathrm { cm } ) / \left( \mathrm { m } ^ { 2 \cdot } { } ^ { \circ } \mathrm { C } \right)$ then the total $R$ -value is $R = \frac { 2.9 \mathrm {~cm} } { 13 \frac { \mathrm { W } \cdot \mathrm { cm } } { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } } + \frac { 15 \mathrm {~cm} } { 2.84 \frac { \mathrm { W } \cdot \mathrm { cm } } { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } } + \frac { 2.0 \mathrm {~cm} } { 13 \frac { \mathrm { W } \cdot \mathrm { cm } } { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } } = 5.66 \frac { \mathrm { m } ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } } { \mathrm { W } }$
The power loss is
$P = \left( 155 \mathrm {~m} ^ { 2 } \right) \times \left( 20 ^ { \circ } \mathrm { C } + 2 ^ { \circ } \mathrm { C } \right) / \left[ 5.66 \left( \mathrm {~m} ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } \right) / \mathrm { W } \right] = 602 \mathrm {~W}$
or
$100 \times ( 789 \mathrm {~W} - 602 \mathrm {~W} ) / ( 789 \mathrm {~W} ) = 23.7 \% \text { reduction. }$

A coal-fired cogeneration station provides electricity and heat to a community of 1000 homes. (a) Each home requires a constant $2.5 \mathrm {~kW} _ { \mathrm { e } }$ , and the generation of electricity is $40 \%$ efficient. If the cogeneration station maintains an output that is just sufficient to satisfy the electrical needs of the community, what is the available total power associated with the waste heat? (b) From part (a), what is the daily coal requirement in $\mathrm { kg }$ ? (c) Each house has a volume of $450 \mathrm {~m} ^ { 3 }$ and maintains an inside temperature of $18.3 ^ { \circ } \mathrm { C }$ . If $90 \%$ of the waste heat is available for heating purposes, what is the minimum (constant) outside temperature for which the cogeneration station can fulfil the heating needs of the community while just satisfying the electrical needs? See Chapter 8 for additional information on heating requirements.

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Question 2

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(a) The total thermal energy generated is $( 1000 ) \times ( 2.5 \mathrm {~kW} ) / ( 0.4 ) = 6.25 \times 10 ^ { 3 } \mathrm {~kW}$
The waste heat is, therefore, $60 \%$ of the total or
$\left( 6.25 \times 10 ^ { 3 } \mathrm {~kW} \right) \times ( 0.6 ) = 3.75 \times 10 ^ { 3 } \mathrm {~kW}$
(b) The total daily thermal energy generated is
$\left( 6.25 \times 10 ^ { 6 } \mathrm {~W} \right) \times ( 24 \mathrm {~h} / \mathrm { d } ) \times ( 3600 \mathrm {~s} / \mathrm { h } ) = 5.4 \times 10 ^ { 11 } \mathrm {~J} / \mathrm { d } = 5.4 \times 10 ^ { 5 } \mathrm { MJ } / \mathrm { d }$
For an energy content of $31 \mathrm { MJ } / \mathrm { kg }$ for coal, the total daily coal requirement is
$\left( 5.4 \times 10 ^ { 5 } \mathrm { MJ } / \mathrm { d } \right) / ( 31 \mathrm { MJ } / \mathrm { kg } ) = 1.74 \times 10 ^ { 4 } \mathrm {~kg} / \mathrm { d }$
(c) From Chapter 8 the heating requirement is $67 \mathrm {~kJ} / \mathrm { m } ^ { 3 }$ per degree day $\left( { } ^ { \circ } \mathrm { C } \right)$ . For 1000 homes of $450 \mathrm {~m} ^ { 3 }$ the total energy requirement is $( 1000 ) \times \left( 450 \mathrm {~m} ^ { 3 } \right) \times \left( 6.7 \times 10 ^ { 3 } \mathrm {~J} / \mathrm { m } ^ { 3 } \right.$ per degree day $) = 3.02 \times 10 ^ { 10 } \mathrm {~J}$ per degree day
The amount of waste heat that is available at $90 \%$ recovery is
$( 0.9 ) \times ( 3.75 \times 106 \mathrm {~W} ) = 3.375 \times 10 ^ { 6 } \mathrm {~W}$
or a total thermal energy per day of
$\left( 3.375 \times 10 ^ { 6 } \mathrm {~W} \right) \times ( 24 \mathrm {~h} / \mathrm { d } ) \times ( 3600 \mathrm {~s} / \mathrm { h } ) = 2.92 \times 10 ^ { 11 } \mathrm {~J}$
This is sufficient to provide heat for
$\left( 2.92 \times 10 ^ { 11 } \mathrm {~J} \right) / \left( 3.02 \times 10 ^ { 10 } \mathrm {~J} \right.$ per degree day $) = 9.7$ degree days
For an inside temperature of $18.3 { } ^ { \circ } \mathrm { C }$ the minimum outside temperature would be
$\left( 18.3 ^ { \circ } \mathrm { C } - 9.7 ^ { \circ } \mathrm { C } \right) = 8.6 ^ { \circ } \mathrm { C }$
This is a relatively high temperature and indicates that this cogeneration approach probably provides an insufficient amount of heat when it satisfies the electricity needs of the community.

R = 0.18 windows in a house are replaced with R = 0.52 windows at a cost of $\$ 250$ per $\mathrm { m } ^ { 2 }$ . Assume that the outside temperature is a constant $5 ^ { \circ } \mathrm { C } [$ a reasonable approximation for a region corresponding to about 4300 degree days per year $\left( { } ^ { \circ } \mathrm { C } \right)$ ] and that heat costs $\$ 0.03$ per MJ. How long will it take to recover the cost of the window replacement? (Do not include the cost recovery factor.)

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Question 3

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The reduction in power loss per m2 which results from replacing the windows is $\Delta P = \left[ \left( 18.3 ^ { \circ } \mathrm { C } - 5 ^ { \circ } \mathrm { C } \right) / 0.18 \right] - \left[ \left( 18.3 ^ { \circ } \mathrm { C } - 5 ^ { \circ } \mathrm { C } \right) / 0.52 \right] = 48.3 \mathrm {~W}$
Over one year this amounts to
$( 48.3 \mathrm {~W} ) \times \left( 3.15 \times 10 ^ { 7 } \mathrm {~s} \right) = 1.52 \times 10 ^ { 3 } \mathrm { MJ }$
At $\$ 0.03$ per MJ, the cost of the energy saved is
$\left( 1.52 \times 10 ^ { 3 } \mathrm { MJ } \right) \times ( \$ 0.03 / \mathrm { MJ } ) = \$ 45.60 \text { per year }$
The payback period for a $\$ 250$ window is $( \$ 250 ) / ( \$ 45.60 / \mathrm { y } ) \approx 5.5 \mathrm { y }$ .

The following table gives specifications for some 2012 automobiles sold in the United States. automobile average gasoline consumption (/100) base price (USD) Honda Civic DX (automatic) 6.9 \ 16,605 Honda Civic Hybrid 5.3 \ 24,134 BMW 750i 13.1 \ 84,300 BMW Active hybrid 750i 11.7 \ 97,000 If it is assumed that maintenance costs are the same for the gasoline and hybrid versions of the same vehicle, use the current price of gasoline in your area to determine how many miles would need to be driven for the better fuel economy of the hybrid to outweigh its higher purchase price. Repeat this calculation for the BMW.

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Question 4

For Figure 17.3, estimate the energy gaps for each of the three LEDs in the white LED package.

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Question 5

Consider the heat losses through the four exterior walls of a house. The house is 9.0 m × 12.0 m and the walls are 3.0 m high. There are 12 windows, each 1 m × 1.6 m. The walls are uninsulated and have an R-value of R = 1.0 and the windows are (uncoated) single pane. The home owner has the option of either upgrading the windows to (uncoated) triple pane or introducing insulation into the walls to increase their R-value to R = 3.5. Which action will provide the greatest benefit? In this problem ignore doors and heat losses through the floor and roof.

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Question 6

A large North American city can have 100,000 street lamps. If these are typically $200 \mathrm {~W}$ lamps and electricity costs $\$ 0.08$ per $\mathrm { kWh }$ , what is the annual electric bill if the lamps are on an average of $12 \mathrm {~h}$ per day? (b) What would be the capital cost to replace 100,000 lamps with $75 \mathrm {~W}$ LED lamps at a cost of $\$ 600$ per lamp? (c) What would be the simple payback period (i.e., do not include capital recovery factor, interest, etc.) for this conversion? (d) Estimate the total $\mathrm { CO } _ { 2 }$ emission reduction over the payback period if the electricity is generated exclusively by coal-fired stations.

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Question 7

A home owner in Maine replaces six 60-W incandescent bulbs in a family room with equivalent CFL's. Using the following information, estimate the net annual energy savings (in dollars) for lighting and heating. The lamps are on an average of 3.5 hours per day and electricity costs $0.105 per kWh. The home is heated with an oil furnace at an efficiency of 87% and home heating fuel costs $0.74 per liter. There are 191 days per year that heat is required and there is no air conditioning.

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Question 8

(a) A future home owner is specifying construction materials for a new home in Edmonton, $\mathrm { AB }$ . The home is heated with electric heat at a cost of $\$ 0.11$ per $\mathrm { kWh }$ . There are $200 \mathrm {~m} ^ { 2 }$ of exterior walls consisting of $5 \mathrm {~cm}$ of wood with space for $15 \mathrm {~cm}$ thick insulation. If fiberglass loose-fill insulation would cost $\$ 2500$ and polystyrene foam sheet insulation would cost $\$ 4000$ , what is the payback period for the additional investment in polystyrene? (b) Repeat part (a) for the same home being built in San Francisco, CA. See Chapter 8 for additional useful information.

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Question 9

Consider typical passenger automobiles in the United States. Calculate the reduction in CO₂ emissions (in tonnes) for a 2008 vehicle compared to a 1966 vehicle during the lifetime of the vehicle (assumed to be 250,000 km).

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Question 10

One approach to cogeneration (electricity and heat) for a community is to design the facility to satisfy heating needs and to import or export electricity as needed. This approach is based on the philosophy that it is much easier to market excess electricity (or purchase it as needed) than to sell excess heat. Consider a typical natural gas-fired cogeneration facility that produces electricity at an efficiency of $40 \%$ and has $50 \%$ of the waste energy available for heating purposes. Discuss the validity of this approach for a northern community (near Anchorage, AK) compared to a southern community (near New Orleans, LA). Provide quantitative comparisons to support your evaluation. Are there other approaches to cogeneration that would be more reasonable for one, or both, of these locations?

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Question 11

From equations (17.4) and (17.5), solve for Tc (i.e., the minimum $\text { temperature at which a heat pump can be effective) in terms of } R , A , P _ { i n } \text {, and } T _ { h } \text {. }$

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Question 12

A 9 W LED lamp produces light at an intensity comparable to a 60 W incandescent bulb. If the lifetime of the bulb is 30,000 hours and electricity costs $\$ 0.12$ per $\mathrm { kWh }$ , what is the total savings in energy costs over the life of the LED? (b) If the LED is used an average of 5 hours per day, how long will it take to realize these savings? What is the average savings per day?

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Question 13

heat pump operates with an outside temperature of −10°C and an inside temperature of +19°C. If the building requires 1.6 GJ of heat per day, what is the average power requirement in kW for the heat pump?

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Question 14

Refer to Figure 2.5. What fraction of waste heat from electricity generation in the United States would be needed to satisfy all of the country's residential fossil fuel use (primarily for heating)?

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Question 15

Compare the overall efficiency of heating a house with oil at 85% efficiency and heating a house with a heat pump with a coefficient of performance of 6 using electricity generated by a heat engine at 35% efficiency.

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Question 16

(a) An old 68% efficient natural gas furnace is used to heat a 400 m³ home in Boston, MA. Estimate the annual savings in $\mathrm { CO } _ { 2 }$ emissions if the furnace is replaced with a $93 \%$ efficient natural gas furnace? (b) Estimate the annual $\mathrm { CO } _ { 2 }$ savings if the old furnace is replaced with an $80 \%$ efficient

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Question 17

(a) From Figure 17.4, estimate the energy gap of a GaN or InGaN LED. (b) Are there other semiconducting materials that could be used (from an energy standpoint) to induce photon emission in a Ce:YAG phosphor?

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Question 18

In a local store, find the price of a 60-W incandescent bulb and CFL and LED bulbs with an equivalent light output. Based on a use of 4 hours per day and an electricity cost of $0.11/kWh, calculate the payback period for each of these bulbs compared to the incandescent.

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Question 19

Compare the primary energy requirement per km travelled for an average 1970 gasoline passenger vehicle in the United States to that for an average 2014 passenger vehicle.

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Question 20

For Figure 17.3, estimate the energy gaps for each of the three LEDs in the white LED package.

Consider typical passenger automobiles in the United States. Calculate the reduction in CO₂ emissions (in tonnes) for a 2008 vehicle compared to a 1966 vehicle during the lifetime of the vehicle (assumed to be 250,000 km).

From equations (17.4) and (17.5), solve for Tc (i.e., the minimum $\text { temperature at which a heat pump can be effective) in terms of } R , A , P _ { i n } \text {, and } T _ { h } \text {. }$

heat pump operates with an outside temperature of −10°C and an inside temperature of +19°C. If the building requires 1.6 GJ of heat per day, what is the average power requirement in kW for the heat pump?

Refer to Figure 2.5. What fraction of waste heat from electricity generation in the United States would be needed to satisfy all of the country's residential fossil fuel use (primarily for heating)?

Compare the overall efficiency of heating a house with oil at 85% efficiency and heating a house with a heat pump with a coefficient of performance of 6 using electricity generated by a heat engine at 35% efficiency.

(a) From Figure 17.4, estimate the energy gap of a GaN or InGaN LED. (b) Are there other semiconducting materials that could be used (from an energy standpoint) to induce photon emission in a Ce:YAG phosphor?

In a local store, find the price of a 60-W incandescent bulb and CFL and LED bulbs with an equivalent light output. Based on a use of 4 hours per day and an electricity cost of $0.11/kWh, calculate the payback period for each of these bulbs compared to the incandescent.

Compare the primary energy requirement per km travelled for an average 1970 gasoline passenger vehicle in the United States to that for an average 2014 passenger vehicle.

Energy Basics

Past, Present, and Future World Energy Use

Fossil Fuel Resources and Use

Environmental Consequences of Fossil Fuel Use

Some Basic Nuclear Physics

Energy From Nuclear Fission

Energy From Nuclear Fusion

Direct Use of Solar Energy

Electricity From Solar Energy

Wind Energy

Hydroelectric Energy

Wave Energy

Tidal Energy

Ocean Thermal Energy Conversion and Ocean Salinity Gradient Energy

Geothermal Energy

Biomass Energy

Energy Storage

Battery Electric Vehicles Bevs

Hydrogen

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Exam 17: Energy Conservation

For Figure 17.3, estimate the energy gaps for each of the three LEDs in the white LED package.

Consider typical passenger automobiles in the United States. Calculate the reduction in CO2 emissions (in tonnes) for a 2008 vehicle compared to a 1966 vehicle during the lifetime of the vehicle (assumed to be 250,000 km).

heat pump operates with an outside temperature of −10°C and an inside temperature of +19°C. If the building requires 1.6 GJ of heat per day, what is the average power requirement in kW for the heat pump?

Refer to Figure 2.5. What fraction of waste heat from electricity generation in the United States would be needed to satisfy all of the country's residential fossil fuel use (primarily for heating)?

Compare the overall efficiency of heating a house with oil at 85% efficiency and heating a house with a heat pump with a coefficient of performance of 6 using electricity generated by a heat engine at 35% efficiency.

(a) From Figure 17.4, estimate the energy gap of a GaN or InGaN LED. (b) Are there other semiconducting materials that could be used (from an energy standpoint) to induce photon emission in a Ce:YAG phosphor?

In a local store, find the price of a 60-W incandescent bulb and CFL and LED bulbs with an equivalent light output. Based on a use of 4 hours per day and an electricity cost of $0.11/kWh, calculate the payback period for each of these bulbs compared to the incandescent.

Compare the primary energy requirement per km travelled for an average 1970 gasoline passenger vehicle in the United States to that for an average 2014 passenger vehicle.

Energy Basics

Past, Present, and Future World Energy Use

Fossil Fuel Resources and Use

Environmental Consequences of Fossil Fuel Use

Some Basic Nuclear Physics

Energy From Nuclear Fission

Energy From Nuclear Fusion

Direct Use of Solar Energy

Electricity From Solar Energy

Wind Energy

Hydroelectric Energy

Wave Energy

Tidal Energy

Ocean Thermal Energy Conversion and Ocean Salinity Gradient Energy

Geothermal Energy

Biomass Energy

Energy Storage

Battery Electric Vehicles Bevs

Hydrogen

Filters

Consider typical passenger automobiles in the United States. Calculate the reduction in CO₂ emissions (in tonnes) for a 2008 vehicle compared to a 1966 vehicle during the lifetime of the vehicle (assumed to be 250,000 km).