APES FRQ calculations without a calculator

Density formula

Density ($\displaystyle D$) is calculated as mass ($\displaystyle m$) divided by volume ($\displaystyle V$): $\displaystyle D = \\frac{m}{V}$.

Convert gallons to liters

1 gallon = 3.78541 liters. To convert, multiply gallons by 3.78541.

What is the formula for energy?

Energy ($\displaystyle E$) can be calculated using $\displaystyle E = mc^2$, where $\displaystyle m$ is mass and $\displaystyle c$ is the speed of light.

True or False: 1 mile = 1.609 kilometers.

True. 1 mile is approximately equal to 1.609 kilometers.

Calculate CO2 emissions: 2 gallons of gasoline.

2 gallons of gasoline yields about 18.6 lbs of CO2. (1 gallon = 9.3 lbs CO2).

Conversion of Fahrenheit to Celsius

Use the formula: $\displaystyle C = \\frac{5}{9}(F - 32)$.

Carbon footprint standard measurement unit?

Measured in tons of CO2 equivalent (CO2e) per year.

Fill in the blank: 1 ton = _____ kg.

1 ton = 907.185 kg.

Water footprint calculation

Calculate total water use, e.g., 1 hamburger requires about 1,800 gallons.

What is primary productivity?

It measures the rate of energy conversion by photosynthetic organisms in an ecosystem.

True or False: Sustainable practices always reduce costs.

False. Upfront costs may be higher, but long-term savings can occur.

What does carbon neutrality mean?

Balancing emitted carbon with carbon offsets or reductions.

Convert acres to hectares.

1 acre = 0.404686 hectares. Multiply acres by 0.404686.

Calculate biodiversity index.

Use Simpson's Diversity Index: $\displaystyle D = 1 - \sum (n/N)^2$, where $\displaystyle n$ = species count, $\displaystyle N$ = total count.

Define ecological footprint.

A measure of human demand on Earth's ecosystems, expressed in area of biologically productive land.

Cause → Effect: Deforestation.

Causes loss of habitat → Leads to biodiversity decline.

What is biocapacity?

It is the ability of an ecosystem to produce resources and absorb waste.

Calculate waste generation per capita.

Total waste divided by population, e.g., 10,000 lbs waste / 100 people = 100 lbs/person.

Energy formula in environmental science?

Energy (E) is calculated using the formula: $\displaystyle E = mc^2$, where m = mass and c = speed of light.

Efficiency formula for energy use?

Efficiency () is calculated as: $\displaystyle \frac{Useful ext{ Energy Output}}{Total ext{ Energy Input}} imes 100$.

True or False: Power is energy per unit time.

True. Power (P) is defined as the rate at which energy is transferred or converted, expressed as $\displaystyle P = \frac{E}{t}$.

What is power measured in?

Power is measured in watts (W), where 1 W = 1 joule/second.

Fill in the blank: 1 kilowatt = ___ watts.

1 kilowatt = 1,000 watts.

Calculate energy consumption: 100 W for 3 hours?

Energy (E) = Power (P) x Time (t) = 100 W x 3 h = 300 Wh.

Difference between renewable and non-renewable energy?

Renewable energy can be replenished naturally (e.g., solar, wind). Non-renewable energy cannot (e.g., coal, oil).

Question: What does 1 kWh represent?

1 kWh represents the energy consumption of 1,000 watts over one hour.

Cause → Effect of higher energy efficiency?

Higher energy efficiency leads to decreased energy consumption and lower emissions.

What is the formula for calculating work?

Work (W) can be calculated as: $\displaystyle W = F imes d$, where F = force and d = distance.

True or False: 1 joule = 1 watt-hour.

False. 1 joule = 1 watt-second; 1 watt-hour = 3,600 joules.

Calculate energy for 2000 W appliance running 2 hours.

Energy (E) = 2000 W x 2 h = 4000 Wh or 4 kWh.

What is the efficiency of a system using 100 J input with 30 J output?

Efficiency = $\displaystyle \frac{30 ext{ J}}{100 ext{ J}} imes 100 = 30\%$.

Difference between direct and indirect energy use?

Direct energy use is measured from consumption (e.g., electricity). Indirect is from production processes (e.g., embodied energy).

Fill in the blank: 1 megawatt (MW) = ___ kilowatts (kW).

1 megawatt = 1,000 kilowatts.

Example of calculating carbon footprint of energy use?

If burning 1 gallon of gasoline (3,000 g CO2): 1 gallon = 33.6 kWh, CO2 = 3,000 g.

What is the formula for calculating population growth rate?

Population Growth Rate = (Births - Deaths) / Total Population × 100

Define species richness.

Species richness is the number of different species present in a specific area or ecosystem.

True or False: Biodiversity indices only consider species richness.

False. Biodiversity indices often consider both species richness and evenness (distribution of individuals among species).

Calculate the biodiversity index: 20 species, 100 individuals.

Biodiversity Index (Shannon Index) = -Σ(pi * ln(pi)), where pi = individuals of species/total individuals.

What does the term 'carrying capacity' refer to?

Carrying capacity is the maximum population size that an environment can sustain indefinitely without degrading.

Fill in the blank: The formula for the change in population size is ΔN = N1 - N0.

ΔN = change in population size, N1 = final population, N0 = initial population.

Compare density-dependent and density-independent factors.

Density-dependent factors: impact varies with population density (e.g., food, disease). Density-independent factors: affect all populations equally (e.g., natural disasters).

What is a common method for estimating species population size?

Mark-Recapture Method: N = (M × C) / R, where M = marked individuals, C = captured individuals, R = recaptured marked individuals.

Cause → Effect: Overfishing.

Cause: Overfishing → Effect: Decreased fish populations and biodiversity loss.

Define the term 'genetic diversity'.

Genetic diversity refers to the variety of genetic characteristics within a species, crucial for adaptability and survival.

True or False: An ecosystem with high biodiversity is more resilient.

True. High biodiversity enhances ecosystem stability and resilience to changes and disturbances.

Calculate the percent change in population: from 200 to 250.

Percent Change = ((Final - Initial) / Initial) × 100 = ((250 - 200) / 200) × 100 = 25%.

What is the significance of the Simpson's Diversity Index?

Simpson's Diversity Index measures the probability that two individuals randomly selected belong to different species, reflecting biodiversity.

Fill in the blank: A species' niche includes its _____ and _____ interactions.

Habitat and biotic interactions, such as predation and competition.

What does the term 'invasive species' mean?

Invasive species are non-native organisms that spread widely in a new environment, often outcompeting native species.

Calculate the total fertility rate given 150 births in 1000 women.

Total Fertility Rate = (Births / Women) × 1000 = (150 / 1000) × 1000 = 150 births per 1000 women.

True or False: High species evenness contributes to ecosystem health.

True. High species evenness means that species are represented by similar numbers, promoting ecosystem stability.

Calculate species diversity using the Shannon Index formula: H' = -Σ(pi ln(pi))

Where H' = Shannon diversity index; pi = proportion of each species; ln = natural logarithm. Example: For 3 species with proportions 0.5, 0.3, and 0.2, H' = -[(0.5 ln(0.5)) + (0.3 ln(0.3)) + (0.2 ln(0.2))].

Definition of recycling rate

The percentage of waste material that is diverted from landfills and recycled. Calculated as: Recycling Rate = (Recycled Material / Total Waste) × 100%

Calculate recycling rate: 500 tons recycled, 2000 tons total waste.

Recycling Rate = (500 / 2000) × 100% = 25%

True or False: Composting reduces landfill waste.

True - Composting converts organic waste into valuable soil, reducing waste volume.

Define waste generation per capita.

The average amount of waste produced by each person in a specific area, often expressed in pounds or kilograms.

Calculate waste generation: 100,000 tons total waste for 1 million people.

Waste Generation per Capita = 100,000 tons / 1,000,000 people = 0.1 tons/person or 200 lbs/person.

What factors influence recycling rates?

- Public awareness - Access to recycling facilities - Economic incentives - Local regulations

Fill in the blank: The formula for total waste generation is ______.

Total Waste = Waste Generated + Waste Recycled + Waste Landfilled

Describe the impact of landfills on resource management.

Landfills consume valuable land and release methane, a potent greenhouse gas. They also waste potential resources that could be recycled.

Difference between biodegradable and non-biodegradable waste.

Biodegradable waste decomposes naturally, while non-biodegradable waste does not and lasts indefinitely.

Calculate total recyclable waste: 50 tons of paper, 30 tons of plastic.

Total Recyclable Waste = 50 + 30 = 80 tons.

What is the environmental benefit of reducing waste?

Reduces pollution, conserves natural resources, and decreases landfill usage.

True or False: All plastics can be recycled.

False - Not all plastics are recyclable due to contamination and varying resin types.

How does urbanization affect waste generation?

Urbanization typically increases waste generation due to higher population density and consumption rates.

Identify the main components of municipal solid waste.

- Food waste - Paper - Plastics - Metals - Glass

Calculate total waste generated: 300 tons, 25% recycled.

Waste Landfilled = Total Waste - Recycled. = 300 - (0.25 × 300) = 225 tons.

List benefits of recycling.

- Reduces waste - Saves energy - Conserves resources - Lowers greenhouse gas emissions

What is a waste audit?

A systematic examination of waste generated by a facility to identify reduction opportunities and recycling potential.

Cause → Effect: Increased recycling programs → ______.

Increased recycling rates and reduced landfill waste.

Define the term 'life cycle assessment'.

A method to evaluate the environmental impacts of a product from raw material extraction through production, use, and disposal.

Calculate total waste diversion rate: 200 tons recycled, 800 tons total.

Diversion Rate = (200 / 800) × 100% = 25%