객관식
Under which of the following conditions does the molar volume of a gas decrease according to the ideal gas law?
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7. Gases
The Ideal Gas Law
객관식
According to the ideal gas law, what is the relationship between pressure and temperature when the volume and amount of gas are held constant?
A
Pressure remains constant as temperature increases.
B
Pressure increases as temperature increases.
C
Pressure and temperature are unrelated.
D
Pressure decreases as temperature increases.
검증된 단계별 안내1
Recall the ideal gas law: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of gas in moles, \(R\) is the ideal gas constant, and \(T\) is temperature in kelvin.
Since the problem states that volume (\(V\)) and amount of gas (\(n\)) are held constant, we can treat \(V\) and \(n\) as constants in the equation.
Rearrange the ideal gas law to express pressure as a function of temperature: \(P = \frac{n \times R \times T}{V}\). Because \(n\), \(R\), and \(V\) are constants, pressure \(P\) is directly proportional to temperature \(T\).
This means that if temperature increases, pressure must also increase proportionally, assuming volume and amount of gas remain unchanged.
Therefore, the correct relationship is: Pressure increases as temperature increases when volume and amount of gas are constant.
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