Question

Question 10 (a) What two conditions have to be satisfied for a sample of a real gas for its be- haviour to be considered ideal? mark (b) Explain why the constant volume molar heat capacity Cy of an ideal diatomic gas is larger than that of an ideal monatomic gas, (5/2) R compared to (3/2) R at moderate temperatures [2 marks Nitrogen is a diatomic gas of molar mass M 28.0g mol-. The ratio of its molar heat capacities at constant pressure and volume is y Cr/Cv 7/5. (You may treat the nitrogen sample described in this question as an ideal gas.) Seven grams of nitrogen initially at pressure of 300 kPa and temperature of 27 °C are cooled at constant volume until the pressure is 100kPa [2 marks (c) What is the original volume of the gas? (d) What is the temperature of the gas after the compression? [I mark] The gas sample is then compressed adiabatically until it reaches its original pressure of 300 kPa [2 marks (e) What is the new volume of the gas? I mark] (f) What is the new temperature of the gas? (g) How much work is done on the gas during the adiabatic compression of the ni trogen? [I mark Finally, the gas is heated isobarically until it returns to its initial volume, completing a cyclic process. (h) Sketch the full three-step cycle on a pV diagram. Show the 100K and 300 K isotherms and identify a feature of the graph corresponding to the total work done in the cycle. [3 marks

Answer 1

Sol" lo a eeal a) At low pressuve amd high temperafure as the dree fraudom is 5 in (omparison to monoctomicas (3 hna the molar atConstot volumu ix R. b)For diatomic i dia tomic are hree dyrec - free dom and to -Yotational free dom Z - c) The number mokusnitnjas i n, O 25 molg 28 (8aked at (onstont valume fom Sine the 300.15 K 233-15) initi temperture T, = (2 P4=n,RTt iil staga Apply ideot eudon. 0.25X 8-314X300 5 300K Pa 30 o fom 0 2.5x8.34X300 IS 2.08 YIO3 m3 300 Y103 d) Fina temperdore fom tion 2 T 300 00.0 4 K