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Task 2 (20 points) * In a lighter, the fuel butane is typically present in two phases. In simplified terms, the fuel container of the lighter shown opposite can be described as a cuboid. The base area is square with a side length of a = 2.0 cm. The height of the cuboid is h = 8.0 cm. In state 1, the fire has generates a temperature of t = 15.0°C. Dera The vapour content of the butane is x1 = 0.07. h The VG Hint: - Round the results to three decimal places (e.g. 1023.300, 58.189 or 0.015) unless otherwise stated. a) 0.5 P] [1 P] b) What is the pressure p in the system in state 1 (in bar)? [ Determine the density of the liquid pli and the density of the gas plin state 1 (both in kg/m3). Determine the total mass m of butane in state 1 (in g). [ At what height hooi is the phase boundary in state 1 (in cm)? c) 2.5 P] d) [2 P] In the following parts of the task, continue calculating exclusively with the following values for state 1. The geometric dimensions do not change. mi pl pi pli 60.07 kg/m3 7.137 kg/m3 1.922 g 567.0 kg/m3 0.1076 2.83 bar Pi 30.0°C e) [1 P] The housing of the lighter can just withstand a pressure of Pberst = 42 bar. At what temperature Tberst is this pressure reached if the total mass mi does not change? (in K)? What is the maximum quantity of 12thalbe added to the butane from state 1 until the container bursts (state 2) k)? f) [4 P]

g) [4 P] After n = 497 candles have been lit with the lighter, they contain only just saturated gas (state 3). The change in state 13 was isothermal. How many millilitres of butane gas left the container per candle on average (in ml)? h) [5 P] What quantity of 13 must be added to the butane for this change of state (1 3) (in kJ)? Notes: - Abbreviation: PG (phase boundary) - Substance data can be taken from the following two tables. If necessary, interpolate linearly. Substance data butane Critical data Butane: tcrit = 152.0"; Pcrit = 228.0 kg/m3; Perit = 37.96 bar Single-phase tp h Cbar 40.0 281.25 275.10 40.0 P kg/m3 58.89 60.07 70.39 95.82 183.21 58.89 233.47 40.0 S S kJ/(kg K) 3.341 3.308 3.075 2.760 2.449 3.430 3.395 3.147 184.08 156.18 299.83 kJ/kg 1161.2 1142.9 1019.9 868.6 731.4 1214.6 1194.5 1059.7 893.5 742.6 40.0 40.0 42.0 42.0 293.19 248.08 60.07 70.39 42.0 193.59 42.0 2.810 95.82 183.21 160.20 42.0 2.472 Two-phase p!! h! kJ/kg 211.6 5.0 kg/m3 3.278 3.873 top' Cbarkg/m3 1.24 595.3 1.48 589.8 1.76 584.3 2.08 578.6 2.43 572.8 kJ/kg 592.4 599.5 10.0 223.4 15.0 606.7 4.549 5.313 20.0 235.3 247.3 259.5 613.8 25.0 6.172 30.0 2.83 567.0 7.137 620.9 628.1 635.2 642.3 35.0 3.28 8.215 271.8 284.2 296.8 561.0 554.9 40.0 3.78 9.418 5