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$\bullet$$\bullet$ In a gas at standard temperature and pressure, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 6 billion people at present)?

$6.1 \times 10^{-6} m$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

University of Sheffield

Lectures

03:15

In physics, the second law of thermodynamics states that the total entropy of an isolated system can only increase over time. The total entropy of a system can never decrease, and the entropy of a system approaches a constant value as the temperature approaches zero.

03:25

The First Law of Thermodynamics is an expression of the principle of conservation of energy. The law states that the change in the internal energy of a closed system is equal to the amount of heat energy added to the system, minus the work done by the system on its surroundings. The total energy of a system can be subdivided and classified in various ways.

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How many molecules are in…

A cube contains a number of gas molecules equal to the population of human beings on earth, so we have number of gas molecules equal to population of human beings. That is 6000000000 point. So 6 multiply 10 to the power 9 molecules. Now we want to calculate the length of side of the cube at cetend temperature and pressure by taking the rial gas equation. P v is equal to n r t, which is so written as p v is equal to n k. T from here we have v that its volume is equal to n k. T upon p here n is equal to 9 multiply 10 to the power 9 molecules multiply here case, boardman's constant having the value of 1.38 multiplied 10 to the power minus 23 joule per molecule per kelvin, and here temperature is 273.15 kelvin upon pressure is 1.01 multiply. 10 to the power 5, pascal, so by multiplying all these numbers, we get volume of the cube equal to 2.23 multiply 10 to the power minus 16 cubic meter. So here we have volume equal to 2.239 multiplied 10 to the power minus 16 cubic meter, as we have a volume of the cube is equal to length multiply length multiply length, so we get volume equal to cubic length. So from here we get. L is equal to cubic root of volume, and the volume here is 2.239 multiply 10 to the power minus 16 cubic meter. So we get length of cube equal to 6.1 times 10 to the power minus 6 meter and there's the answer.

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