Question

A gas cylinder containing carbon dioxide, CO2, 85% by volume, and nitrogen, N2, 15% by volume has a volume of 2.2 m and is kept at a temperature of 20°C. You may assume the gas mixture is ideal. 0 Calculate the pressure in kPa in the cylinder when it contains 50 kg of gas. [2 marks] After a certain amount of gas has been used, the pressure decreases by 150 kPa. Calculate the mass of gas used. [2 marks] (b) The complete differential of entropy, ds, for a closed thermodynamic system of constant composition is given by Equation 1 below in terms of the complete differentials of pressure, dp, and temperature, dТ. In Equation 1, V is the system volume and Cp the system heat capacity at constant pressure. (1) dS = - 14 T w (1) (1) (ii ) Starting from Equation 1, derive an equation for the change in entropy, as, of one mole of an ideal gas when the pressure changes from an initial pressure pa to a final pressure p2 and the temperature changes from an initial temperature of T. to a final temperature of T2. Explain any assumptions you have made in deriving the equation. [5 marks] Describe a method to calculate a dew point pressure at a specified temperature for a stream with a given vapour composition. [3 marks] (iii) A compressor is used to compress helium gas from an initial pressure of 150 kPa to a final pressure of 550 kPa. The temperature of the helium gas in the feed to the compressor is 290 K. The heat capacity of helium gas at constant pressure may be taken as 20.9 J mol-K! If the compressor operates adiabatically and perfectly reversibly, what is the final temperature of the helium gas? [2 marks] Sketch, in a qualitative way, a pressure versus temperature phase diagram for a single component. On your sketch clearly label the following: () Solid-liquid phase coexistence line. (ii) Solid-vapour phase coexistence line. Liquid-vapour phase coexistence line. (iv) Triple point (v) Critical point [You do not need to perform a calculation or present numerical values.] [6 marks] (c) Relative atomic masses: H = 1.0, C = 12.0, N = 14.0; standard pressure = 100 kPa = 1 bar; 0°C = 273 K