Question

At 400 K, the following graph is obtained for \( x \) moles of an ideal gas. \( x \) is equal to (R = gas constant, P = pressure, V = volume)

• A. \( \frac{m}{400R} \)
• B. \( \frac{400R}{m} \)
• C. \( 400mR \)
• D. \( \frac{1}{400R} \)

Hint:

For ideal gases, \( PV = nRT \) is the equation of state. The slope of the P vs. \( 1/V \) graph gives the relationship between the pressure, temperature, and volume at constant temperature.

Answer 1

The Correct Option is A

The equation of the graph at constant temperature for an ideal gas follows Boyle's law, which is: \[ PV = nRT \] Given the graph, it suggests a straight-line relation between pressure and the inverse of volume, which implies that the slope \( m \) of the line is related to the equation. The correct relation would be: \[ m = \frac{1}{400R} \] Thus, the slope is \( \frac{m}{400R} \).