An ideal gas undergoes a thermodynamic process in which its pressure is directly proportional to its volume ( P V ). Which of the following correctly describes the shape of the graph showing the variation of its absolute temperature ( T ) on the y-axis with volume ( V ) on the x-axis?

Step-by-step solution

Given that pressure is directly proportional to volume, we can write P = kV , where k is a positive constant. From the ideal gas equation, we have PV = nRT . Substituting P = kV into the ideal gas equation gives: (kV)V = nRT kV^2 = nRT T = ( k nR )V^2 This equation is of the form y = cx^2 , which represents a parabola opening upwards (towards the y-axis, which is the temperature axis). Therefore, the graph of T versus V is a parabola opening towards the temperature axis. Answer: A parabola opening towards the tempe