A graph is plotted between pressure ( P ) on the y-axis and density ( ) on the x-axis for a given mass of an ideal gas. The graph shows three straight lines passing through the origin, corresponding to three different constant temperatures T₁ , T₂ , and T₃ . If the line for T₁ is the steepest and the line for T₃ is the least steep, which of the following represents the correct relationship between the temperatures?

Step-by-step solution

From the ideal gas equation, PV = nRT . We know that the number of moles n = m M and density = m V . Substituting these, we get P = ( m M ) RT V P = ( RT M ) . For a P versus graph, the equation is of the form y = mx , where the slope m = RT M . Thus, the slope of the line is directly proportional to the temperature T . Since the line for T₁ is the steepest (maximum slope) and T₃ is the least steep (minimum slope), it follows that T₁ > T₂ > T₃ . Answer: T₁ > T₂ > T₃