Consider a reversible thermodynamic process involving one mole of ideal gas represented by a line on the P-V diagram connecting two states X ( 4 bar, 1 L, T₁ ) and Y ( 1 bar, 2 L, T₂ ) as shown in the figure: During the process the change in temperature (in K) as a function of volume (in L) is best represented as:

Step-by-step solution

The process is represented by a straight line in the P-V diagram passing through the points (1, 4) and (2, 1) . The equation of this line is given by P - P₁ = P₂ - P₁ V₂ - V₁ (V - V₁) . Substituting the values, we get: P - 4 = 1 - 4 2 - 1 (V - 1) P - 4 = -3(V - 1) P = -3V + 7 For one mole of an ideal gas, the equation of state is PV = RT . Substituting the expression for P , we obtain the temperature T as a function of V : (-3V + 7)V = RT T = 1 R (7V - 3V^2) This represents a downward-opening parabola in the T-V pl