Ideal gas at constant pressure

The molar heat capacity of an ideal gas at constant pressure is greater than that at constant volume the two quantities are related by Eq. 13. 

Similarly, the molar heat capacity at constant pressure, Cp, is calculated by examining the heating of a monatomic ideal gas at constant pressure from temperature Ti to Tx- Experimentally, such a process can be performed by placing the gas in a cylinder with a piston that moves out as the gas is heated, keeping the gas pressure equal to the outside pressure. In this case,... 

It follows, therefore, that when gases approximate to ideal behavior, i.e., at very low pressures, the differences in their thermometric properties disappear. This fact presents the possibility of devising a temperature scale which shall be independent of the thermometric substance, the latter being a hypothetical ideal gas. Such a scale is the so-called absolute ideal gas scale, in which the (absolute) temperature is taken as direcUy proportional to the volume of a definite mass of an ideal gas at constant pressure or to the pressure at constant volume. For convenience, the magnitude of the degree on the absolute scale is usually taken to be the same as on the centigrade scale ( 2b), so that the absolute temperature T on the ideal gas scale is given by... 

As a first exarhple, we will consider the reversible compression of an ideal gas at constant pressure. Suppose that we have 1 mol of an ideal gas confined in a cylinder with a piston, at a pressure of Pu a volume of and a temperature (in kelvins) of... 

Charles s law states that the volume of a given amount of an ideal gas at constant pressure varies directly with its temperature (in kelvins). V = bT... 

Charle s Law is the empirical relationship, which states tliat which states that for an ideal gas at constant pressure, its volume is proportional to its absolute temperature. This relationship applies to ideal gases only. Real gases deviate considerable form this ideal relationship. 

As the pressure of an ideal gas increases, its volume decreases proportionately. Charles law describes the relationship between the volume and temperature of an ideal gas at constant pressure ... 

In a linear relationship there is a directly proportional relationship between the two variables. The relationship is described by the formula y = mx + c, where c is the intercept on the y-axis and m is the slope or gradient of the line (Figure 11.25). This is characteristic of Charles law the relationship between the volume and temperature of an ideal gas (at constant pressure) (Chapter 1). 

Now we can take advantage of these expressions to obtain the following relation between specific heats of the the ideal gas at constant pressure and constant volume ... 

For an ideal gas at constant pressure, for light propagating along the Z axis... 

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