An ideal gas ( = 1.67 ) is taken through the process abc shown in the figure. The temperature at the point a is 300 K . Calculate the change in the internal energy of the gas in the process.

Step-by-step solution

From the given graph, the pressure and volume at the initial state a and final state c are: P_a = 100 kPa = 10^5 Pa V_a = 100 cm ^3 = 10⁻⁴ m ^3 P_c = 200 kPa = 2 10^5 Pa V_c = 150 cm ^3 = 1.5 10⁻⁴ m ^3 The product of pressure and volume at these states can be calculated as: P_a V_a = 10^5 10⁻⁴ = 10 J P_c V_c = 2 10^5 1.5 10⁻⁴ = 30 J The change in internal energy U for an ideal gas depends only on the initial and final states and is given by: U = P_c V_c - P_a V_a - 1 Substituting the given values ( = 1.67 ): U = 30