Question

(9%) Problem 7: A bicycle tire has a pressure of 7.15 x 10 Pa at a temperature of 19.5°C and contains 2.00 L of gas. What will its pressure be, in pascals, if you let out an amount of air that has a volume of 105 cm'at atmospheric pressure and at the temperature of the tire? Assume tire temperature and volume remain constant. Grade Summary Deductions 0% Potential 100% sino tan) 78 9 HOME Submissions cotan asino acos ETA 4 5 Attempts remaining: 50 6 (o per attempt atano acotan sinh 123 detailed view cosho tanho cotanh + - 0 Degrees O Radians VOCE cos Submit Hint Fendrick I give up! Hints: dedactica per in. Hints remaining 1 Feedback: 0 deduction per feedback MacBook 200 DOO . FS DHI DD

Answer 1

7 ) Initial pressure, PE 7.15 x 105 Pa Initial tempenature, Te = 19.5°C =(19.5 +373) K = 292.5K Since, temperature remains constant, T Initial volume, Vé = 2L = 2x153 m3 = final volume, vf [:'volume remains constant Tf 292.5 K Vout 105cm3 = 105 x 156 m3 Pout = Patm = 1.04 x 105 Pa 幽 From Ideal gas's lawo, PV = nRT Ру NT FR = constant Pevi Pf Vf = R Me T nf Tf Ve=Vf and Te = Tf رفر No Pe Pf nf ni P4 = nf Pi ni 0 Initial number of molecules, nie- Pevi = nq R T Pevi (7.15 X10% pa) (2x109 m2) 18.31 J/molk) (292.5K) ni = 0.588 mol ni RT

Number of moles of exausted air, Pout (1.04 x 105 pa) (105x 10 (8.31 J/molk) 292.5) -6 Vout 6 m3) nout R Tout Tout Nout 4.363 x 10 3 mol Now, the final number of molecules, ng ne -nout = f {0-588 --(4-363X173)} mol nf = 0.5836 mol From equation PA nf Pi ni (0.5836 mol (0.588 mol) x (7-15x105 100 Pa) Pe 7:096 x 105 pa ... The final Pressure is: 7.096X105 Pal Ans.

When I calculated n(out) I take T(out) = T(i) since the tire and its air are in thermal equilibrium with the environment surrounding it.