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Chapter 9: Problem 1333

Under constant temperature, graph between \(\mathrm{p}\) and \((1 / \mathrm{V})\) is (A) Hyperbola (B) Circle (C) Parabola (D) Straight line

Short Answer

Expert verified
The relationship between pressure (\(p\)) and the inverse of volume (\(\frac{1}{V}\)) under constant temperature can be represented by the equation \(p = \frac{k}{V}\), which shows a direct relationship. Thus, the graph between \(p\) and \(\frac{1}{V}\) is a straight line. The correct answer is (D) Straight line.

Step by step solution

01

Boyle's law can be represented by the following equation: \[pV = k\] Where: - \(p\) is the pressure of the gas - \(V\) is the volume of the gas - \(k\) is a constant that depends on the amount of gas and the temperature As the temperature is kept constant, the value of \(k\) is also constant in this case. #Step 2: Rearrange the equation to show the relation between p and 1/V#

Since we need to find the graph between p and (1/V), we'll need to rewrite the equation in terms of these two variables. To do so, we take the inverse of both sides of the equation: \[\frac{1}{p}\frac{1}{V} = \frac{1}{k}\] Multiplying both sides of the equation by \(V\), we get: \[\frac{1}{p} = \frac{V}{k}\] Now, multiplying both sides of the equation by \(p\), we get the final equation: \[p = \frac{k}{V}\] #Step 3: Identify the type of graph between p and 1/V#
02

The equation that we obtained in the previous step is: \[p = \frac{k}{V}\] From this equation, we can see that the relationship between pressure and the inverse of volume is a direct relationship, as one goes up, the other also goes up. This is a characteristic of a straight line. Hence, the graph between pressure (\(p\)) and the inverse of volume (\(1/V\)) under constant temperature is a straight line. #Step 4: Choose the correct answer#

Based on our analysis, the correct answer is: (D) Straight line

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Most popular questions from this chapter

\- decrease the volume of gas by \(\supset \%\) at constant temperature the pressure should be (A) Increased by \(5.26 \%\) (B) Decreased by \(5.26 \%\) (C) Decreased by \(11 \%\) (D) Increased by \(11 \%\)

Pressure of an ideal gas is increased by keeping temperature constant what is the effect on kinetic energy of molecules. (A) Decrease (B) Increase (C) No change (D) Can't be determined

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