What is the relation between a ton and a kilocalorie?

Answer 1

No relation The short answer is none, a ton is a measure of mass and a kilocalorie is a measure of energy and they are different things. BUT weight is the force applied to a given mass by gravity, and energy and mass are interchangeable by Einstein's famous equation E=mc^2 or energy equals mass times the speed of light squared. Thus a relationship can be shown. Let's start by converting everything to metric units which are easier to deal with mathematically. A ton is 2000 pounds. A kilogram weighs 2.2 pounds. Thus the mass, in metric units, of one ton is 2000/2.2=909.1 kilograms. The kilocalorie (1000 calories) is equal to 4186 joules of energy. The basic units of energy are mass times speed squared. The joule, being a metric unit, is equal to 1 kilogram times one meter squared per second squared or 1Kgm^2/s^2. The speed of light, in metric units, is 2.998x10^8 m/s. So, if we took one ton's worth of mass and converted it into energy (the sun does this several thousand times a second) what would we get? 909.1 Kg x (2.998m/s)^2 = 8.171x10^19 Kgm^2/s^2 or joules. Dividing that by 4186 to convert from joules to kilocalories gives us 1.952x10^16 kilocalories. So, one ton is equivalent to 19,520,000,000,000,000 kilocalories. That's nineteen quadrillion, five hundred twenty trillion. If we do the calculation the other way and convert one kilocalorie into mass then we get 4186 J/(2.998 x 10^8 m/s)^2 = 4.657x10^-14 kg. Dividing that by 909.1 to convert it into tons gives 5.123 x 10^-17 tons or 0.00000000000000005123 tons. By the way, the word calorie is used in two different ways by scientists. The standard calorie that is used by physicists and chemists is only equal to 4.186 joules. Biologists and nutritionists use the Large Calorie which is equal to one thousand standard calories or one kilocalorie (4186 joules). So, when you say, "That cheeseburger has 800 calories in it," you really mean 800 kilocalories. Unless the question poster meant one ton [explosive] One ton [explosive] is equivalent to one million kilocalories [thermochemical].