# 6.9 The ideal gas law  (Page 5/11)

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The ideal gas law can be considered to be another manifestation of the law of conservation of energy. Work done on a gas results in an increase in its energy, increasing pressure and/or temperature, or decreasing volume. This increased energy can also be viewed as increased internal kinetic energy, given the gas’s atoms and molecules.

## The ideal gas law and energy

Let us now examine the role of energy in the behavior of gases. When you inflate a bike tire by hand, you do work by repeatedly exerting a force through a distance. This energy goes into increasing the pressure of air inside the tire and increasing the temperature of the pump and the air.

The ideal gas law is closely related to energy: the units on both sides are joules. The right-hand side of the ideal gas law in $\text{PV}=\text{NkT}$ is $\text{NkT}$ . This term is roughly the amount of translational kinetic energy of $N$ atoms or molecules at an absolute temperature $T$ . The left-hand side of the ideal gas law is $\text{PV}$ , which also has the units of joules. We know from our study of fluids that pressure is one type of potential energy per unit volume, so pressure multiplied by volume is energy. The important point is that there is energy in a gas related to both its pressure and its volume. The energy can be changed when the gas is doing work as it expands—something we explore in"Heat and Heat Transfer Methods"—similar to what occurs in gasoline or steam engines and turbines.

## Problem-solving strategy: the ideal gas law

Step 1 Examine the situation to determine that an ideal gas is involved. Most gases are nearly ideal.

Step 2 Make a list of what quantities are given, or can be inferred from the problem as stated (identify the known quantities). Convert known values into proper SI units (K for temperature, Pa for pressure, ${\text{m}}^{3}$ for volume, molecules for $N$ , and moles for $n$ ).

Step 3 Identify exactly what needs to be determined in the problem (identify the unknown quantities). A written list is useful.

Step 4 Determine whether the number of molecules or the number of moles is known, in order to decide which form of the ideal gas law to use. The first form is $\text{PV}=\text{NkT}$ and involves $N$ , the number of atoms or molecules. The second form is $\text{PV}=\text{nRT}$ and involves $n$ , the number of moles.

Step 5 Solve the ideal gas law for the quantity to be determined (the unknown quantity). You may need to take a ratio of final states to initial states to eliminate the unknown quantities that are kept fixed.

Step 6 Substitute the known quantities, along with their units, into the appropriate equation, and obtain numerical solutions complete with units. Be certain to use absolute temperature and absolute pressure.

Step 7 Check the answer to see if it is reasonable: Does it make sense?

Liquids and solids have densities about 1000 times greater than gases. Explain how this implies that the distances between atoms and molecules in gases are about 10 times greater than the size of their atoms and molecules.

Atoms and molecules are close together in solids and liquids. In gases they are separated by empty space. Thus gases have lower densities than liquids and solids. Density is mass per unit volume, and volume is related to the size of a body (such as a sphere) cubed. So if the distance between atoms and molecules increases by a factor of 10, then the volume occupied increases by a factor of 1000, and the density decreases by a factor of 1000.

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do the negative slope of production possibility curve sloped to show trade offs in production of two goods?
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according to professor Richard lipsey economics is a social science that concerns with the way society has employ scarce productive resources in other to achieve a certain conditions of living
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what is the practical significance of cross price elasticity of demand?
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what is the practical significance of cross price elasticity of demand?
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economics is a social science that deals with human behaviour relating with end and scares means
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according to working definition of economics by professor Richard lipsey economics is a social science that concerns with the way society has choice to employ scarce productive resources in other to achieve a certain living conditions
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why is economics not a pure science?
it is not a pure science because it only studies human behavior
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economics is a social science cause it is relating to ends and scares means🙂
Okafor
economics is not a pure science because it studies about human behaviour scarcity want and needs of human beings and the critical thinking of human beings it can be said not to be a pure science because it cannot be manipulated because you don't know humans minds, humans minds are unpredictable
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economics is not a pure science because it studies about human behavior scarcity want and needs of human being .and the critical thinking of human being. last science can be manipulated but economics cannot because you don't know humans minds, humans min
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4. It is a hot day, and Bert is thirsty. Here is the value he places on each bottle of water: Value of first bottle $7 Value of second bottle$5 Value of third bottle $3 Value of fourth bottle$1 a. From this information, derive Bert’s demand schedule. Graph his demand curve for bottled w
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The law of diminishing marginal utility state that as a consumer consumes a successive units of a commodity, a point is eventually reached where consumption of additional unit yields less satisfaction.
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other things can be equal an certain amount paid for the goods by consumer in the market called demand.
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demand is the amount of a commodity a consumer is willing and able buy at a given price at a particular point in time
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Demand is the quantity of commodity a consumer is willing and able to buy at a given price and a particular time.
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demand can be defined as the willingness and ability of a consumer to purchase goods or services at a given price in a particular time
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economics is a social science subject, which study human behaviors as a relationship btw end ND scarce means
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Utility is the satisfaction a consumer derives from consuming a particular commodity.
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