Question 11

Which of the following shows the correct relationship between the pressure $$P$$ and density $$\rho$$ of an ideal gas at constant temperature?

Solution

$$PV = nRT$$

$$PV = \left(\frac{m}{M}\right)RT$$

$$P = \left(\frac{m}{V}\right) \frac{RT}{M}$$

$$P = \rho \frac{RT}{M}$$

The plot of pressure ($$P$$) versus density ($$\rho$$) at a constant temperature results in a straight line starting from the origin, indicating that pressure is directly proportional to density. The correct relationship is represented by the straight-line graph in Option D.

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