CALC A cylinder with a piston contains 0.150 mol of nitrogen at 1.80 X 105 Pa and 300 K. The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure. (a) Show the series of processes in a pV-diagram. (b) Compute the temperatures at the beginning and end of the adiabatic expansion. (c) Compute the minimum pressure.

Solution 66P a) During the isobaric compression, the P-V diagram will be, During the adiabatic expansion, b) Step 1: The initial temperature T w0s 300 K. The initial pressure was P = 0.8 × 10 Pa.5 N = 0.150 mol. The volume gets halved to it’s original volume isobarically. So, V = V / 2. 1 0 From the ideal gas law, P 0 =0nRT ----0-------------(1) And P V = nRT 1 1 1 P V 0 20= nRT -----1--------------(2) From equation (1) and (2), 2T 1 T =0300 K (given) T = 300 K/2 = 150 K . 1 This is the temperature in the beginning of the adiabatic expansion.