Engineer Kažimír

Comical errors, disputes and plots arise when converting physical units. The core of today's dispute was the price of natural gas. The unit was changed - from the natural unit of cubic meter of gas to the unit kWh. The goal was to be able to compare the prices of electricity and the energy contained in gas. In short, the goal of the change was to show that gas is 2-3 times cheaper than electricity.

Engineer Kažimír says that during their tenure, there was a large decline in the price of natural gas. The price went from 0.46 €/m³ to € 0.0425/kWh. Calculate:

1. How many percents do the gas price fall if we do not consider the unit in which the price is shown?
2. Transform unit 1 kWh of energy to MJ
3. If you are considering a calorific value of natural gas was 3.91×10⁷ J/m³, calculate how much MJ is released by burning one cubic meter of gas
4. What is the conversion factor combustion heat of natural gas to kWh?
5. Calculate how many percent dropped the price of gas when considering the calorific value of gas.

Mr. engineer Kažimír does not have a bit of common sense when comparing gas prices in €/kWh to the price quoted €/m³.

Prove that one cubic meter is 46 cents a kilowatt-hour and costs 4.25 cents, so it is the same price.

Correct answer:

Gas prices fell numerically by:  90.8 %
1 kWh =  3.6 MJ
combustion of m³ of gas gives heat:  39.1 MJ
combustion of m³ of gas gives heat:  10.9 kWh
Gas prices fell by:  0 %

Step-by-step explanation:

$p=100\%\cdot (1-\frac{0.0425}{0.46})=90.8\%$

$1kWh=\frac{1000\cdot 3600}{1000000}=3.6\text{MJ}$

$Q_1=\frac{3.91\cdot 10^7}{10^6}=39.1\text{MJ}$

$Q_2=\frac{3.91\cdot 10^7}{10^6\cdot 3.6}=10.9\text{kWh}$

$p_2=100\%\cdot \frac{0.46-0.0425Q_2}{0.46}\doteq 0\%$

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