calories (cal) to US Therms (thm) conversion

What is calories?

Calories are a unit of energy, historically defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius. While the "calorie" is still commonly used, the kilocalorie (kcal), also known as the "large calorie" or "food calorie," is more prevalent when discussing dietary energy. In the International System of Units (SI), the joule (J) is the standard unit of energy.

Types of Calories

• Small calorie (cal): The amount of energy required to raise the temperature of 1 gram of water by 1°C.
• Large calorie (Cal) or Kilocalorie (kcal): The amount of energy required to raise the temperature of 1 kilogram of water by 1°C. This is the calorie commonly referred to in nutrition.

The relationship between these units is:

$1 \text{ Cal} = 1 \text{ kcal} = 1000 \text{ cal}$

Calorie to Joule Conversion

Since the joule is the SI unit for energy, it's useful to know the conversion factor:

$1 \text{ cal} \approx 4.184 \text{ J}$

$1 \text{ kcal} \approx 4184 \text{ J}$

Historical Context

While not directly related to a specific law, the development of calorimetry (the science of measuring heat) was crucial to understanding calories. Scientists like Nicolas Clément and later Wilbur Olin Atwater, a pioneer in nutrition science, contributed significantly to establishing calorie values for different foods. Atwater's work in the late 19th and early 20th centuries was instrumental in developing the calorie system used in nutrition today.

Real-World Examples and Calorie Values

• Food:

  • One medium apple (approx. 182g): ~95 kcal
  • One slice of whole wheat bread: ~70 kcal
  • A can of soda (355ml): ~150 kcal

• Energy Expenditure:

  • A 150-pound person running for 30 minutes at 6 mph burns approximately 340 kcal.
  • Sleeping for 8 hours burns roughly 50 kcal per hour, totaling around 400 kcal.

• Other Quantities:

  • Gasoline: 1 gallon of gasoline contains approximately 31,000 kcal.

Measuring Calories in Food

Calories in food are typically determined using a bomb calorimeter. This device measures the heat released when a food sample is completely burned inside a closed chamber surrounded by water. The temperature increase of the water is then used to calculate the calorie content of the food. The caloric content in the three macronutrients are as follows:

• Carbohydrates: 4 kcal/gram
• Proteins: 4 kcal/gram
• Fats: 9 kcal/gram

What is the US Therm?

The US therm is a unit of heat energy used primarily in the natural gas industry to measure and bill the energy content of gas supplied to homes and businesses in the United States.

Definition

The US therm is defined as 100,000 British thermal units (BTU) based on the 59 °F (15 °C) BTU:

$$1\ \text{thm} = 1.05480 \times 10⁸\ \text{J}$$

More precisely, the US therm equals exactly 105,480,400 joules (about 105.48 MJ). It should not be confused with the slightly larger UK therm, which is based on the International Table BTU and equals 105,505,585.257 J.

Origin and History

The therm entered use in the 20th century as gas utilities shifted from billing customers by volume to billing by delivered energy, since the heating value of natural gas varies with its composition. Combining "therm" (from the Greek thermē, heat) with a fixed BTU count gave a convenient billing unit roughly equal to the energy in 100 cubic feet of typical natural gas.

Law and Notable Facts

In the United States the therm is a legally recognized commercial unit for natural gas sales. Gas meters record volume in hundreds of cubic feet (ccf), which utilities multiply by a "therm factor" reflecting the gas's actual heat content to convert to therms for billing.

Real-World Examples and Conversions

• A typical US home uses roughly 500 to 1,000 therms of natural gas per year for heating, cooking, and hot water.
• 1 therm equals about 29.3 kilowatt-hours of energy.
• Burning 1 therm of natural gas releases approximately 105.5 MJ of heat, enough to run a 20 kW furnace at full output for about 88 minutes.