Energy and Society

Week 4 Section Notes

Agenda

1. Energy conversion and efficiency (15 minutes)

2. Combustion chemistry (35 minutes)

1.Energy Conversion

Let’s continue practicing energy conversions to understand how much energy it takes to raise the temperature of a substance. The equation to describe this energy transfer is the following:

Q=Cpm∆T

Q is the amount of energy transfer to a substance (in J), with mass m (in g) when its temperature is raised by ∆T (ºC) and the specific heat of the substance is Cp(in J/g•ºC). The specific heat of a substance is the amount of heat per unit mass required to raise the temperature by 1 degree Celsius.

Practice Problem1: Could the chemical energy content in one teaspoon of sugar be sufficient to heat a cup of water to prepare tea or coffee? Assume that there are 4 grams of sugar in a teaspoon and that 1/20 of a gram of sugar contains about 1,000 J of chemical energy. One cup ~ 250 ml and one teaspoon ~5ml. It takes 4.2 J (or one calorie) to raise the temperature of 1 gram of water by 1 °C.

Before solving the question, take a guess at the answer. Roughly speaking, does this amount of sugar have abundant energy for heating a cup of water, about the right about of energy, or nowhere near enough?

How hot could we make the water by using the sugar for fusion? Use the famous mass-energy equivalence formula (E=mc2), and assume it takes 2 J to raise the temperature of 1 gram of water by 1 °C[1]. What kind of units do you need to make this equation work properly if energy is expressed in terms of joules?

A joule, defined with SI units, is a kg-m2/s2. If c, the speed of light, is 2.99x108 m/s, then our mass value should be expressed in kg. 4 g = 0.004 kg

2. Combustion Chemistry

What is a mole? 1 mole of a substance always contains 6.02×1023 or Avogadro’s number of representative particles.

You can look up each element’s molecular weight on the Periodic Table. Most commonly used molecular weights for this class:

H – 1 g/mol

O – 16 g/mol

C – 12 g/mol

N – 14 g/mol

1 mole of an ideal gas occupies 22.4L or 22.4×10-3m3 at STP (Standard Temperature and Pressure or 0 ºC and 1 bar).

Alternatively, there are 44.6 mol of ideal gas in 1 m3:

= 0.0446 x 103 mol/m3 = 44.6 mol/1 m3

Simple combustion (in a pure oxygen environment)

CH4 + 2O2 CO2 + 2H2O

Real combustion:

CH4 + α(O2 + 3.78N2)  CO2 + (n/2) H2O + 3.78αN2

Why is air represented as O2 + 3.78N2?

Although air has other components in addition to oxygen and nitrogen, approximate volumetric shares of oxygen and nitrogen can be considered to be O2 = 21% and N2 = 79%.

0.21/0.78 ≈ 3.78

Volumetric ratio is ratio of moles, not mass or molecular weight.

Solving combustion chemistry problems:

  1. Balance the chemical equation to make sure mass is conserved (same number of atoms on both sides of the equation).
  2. Converting the starting grams of fuel into moles, based on the fuel’s grams/mole value.
  3. Use the molecular (molar) ratios of the solved equation to calculate the moles of resulting CO2 emissions.
  4. Convert the moles of CO2 to grams, using the grams/mole value of CO2.

Practice Problem 1: What mass of carbon dioxide would be produced if 100g of butane (C4H10) are completely oxidized to carbon dioxide and water?

Note 1: Weight of CO2 is about three times that of butane

Note 2: Although 100g can have 1,2, or 3 significant figures, use the lowest number of significant figures for problem sets.

Practice Problem 2: Worldwide combustion of methane CH4 (natural gas) provides about 1.3×1017kJ of energy per year (BP estimates for 2013). If methane has an energy content of 39×103kJ/m3 (at STP), what mass of CO2 is emitted into the atmosphere each year? Also, express that emission rate as metric tons of carbon (not CO2).

Note: 1 mole of ideal gas has a volume of 22.4 L at STP i.e. 44.6 moles/ m3

Practice Problem 3: Diesel (CH1.8) engines are used to generate electricity on a stand by basis (i.e. when there is a power cut) or in remote areas where there is no access to electricity.

Trivia: Number of people in the world without access to electricity is approximately 1.2 billion. That’s 20% of the world’s population. Most don’t have access to diesel engines, and use kerosene for lighting. In addition, millions have unreliable access to electricity, especially in the developing world, and diesel engines are common as a backup source of electricity. How polluting AND expensive!!!

Balance the combustion equation for diesel. How much carbon is emitted for every kg of diesel burned? What is the mole fraction of CO2 in the exhaust?

Practice Problem 4:[2] Claim: a regular-sized vehicle, driven an average amount, will emit its own weight (about 2 tonnes) in CO2 each year. Perform a back-of-the-envelope calculation to verify (or refute!) this claim. Assume the vehicle is fueled by octane (C8H18) and use basic combustion chemistry to inform your calculations.

Assume:10,000 mi/yr driven

40 mpg fuel economy (a new car, as opposed to an average-aged car)

1

9/7/2015

[1]The specific heat of water changes depending on its temperature, and in its gaseous form as water vapor, the value is lower than that of liquid water. With the galactic temperatures we’re contemplating here, there isn’t really a single sensible number to plug in. Given the extreme scenario we’re considering here, there are lots of factors that we’re not considering with this simple calculation.

[2]This question is slightly more advanced that material covered on the current problem set. It’s here as a challenge problem, so something to come back to in a week or two.