Question

(4) (24 pts): A gas of nitrogen, N2, is in thermal equilibrium. a) The average kinetic energy of a molecule of N2 is mVrms/2. Assume N2 to be a diatomic gas with only three activated degrees of freedom. Write an expression for Vrms as a function of the temperature. b) Assume T = 20 °C. Compare Vrms to the escape velocity of a molecule from the surface of the Earth. Explain whether we need to worry that Earth might lose its Nitrogen in the near future. c) The N2 gas is taken through the cyclic process described in the figure below. Find the net energy transferred to the system by heat during one complete cycle. d) What if the cycle is reversed? That is what is the process follows the path ACBA instead. What is the net energy input per cycle by heat? P(hpa) lu=1.66x10-27 kg B An=14 8 6 4 А . () 6 8 10

Answer 1

a Avera rage Kinetic energy of a molecule of Ny = tm verrons By Equipartition theorem of energy, average Kinetic a molecole per degrees of freedom =ART. TA Ta temperature, R= universal constant gas 38.314 I mollk Avogadro Number energy of NA e kinetic N2 has three activated degrees of freedom, average energy ska 3x ZRT I'm warms 올RT Soms = (Answer) 61 3 RT NAM CScanned with CamScanner

b T220c =(20+273) k 273) = 293K 28 amu mass of No molecore 28 1066x10 9427 kg Norms M2 ЗRT Na.m [ ** 3.314 * 293 Y2 6:022x1023x28x166 x 1027 5. 109x10² m Is 510.9 m/s Norms . Escape velocity of earth 11.2 kms = 11.2 x 103 mis 510.9 Ë0-045 Nescape 11.2 x 103 Narms. << Veseape, there is less escape from earth. ". We need not. worry that Earth might ght lose N2 in future, as chance for Nz to near CScanned with CamScanner

from first law of thermodynamics dq = dor do its state, in returns to its initial internal смета is en AUS 0 onchanged (state function) བ ནི ༢ 9.P (kPa) from figure, 8 work done a area of 4 ABC 2 10 vimos) E ACBC = $(10-6)-(8-2) INJ - ²x4x4 kJ -8KT 109 - 8kg (Answery) @ It the cycle is reversed, net energy input "per cycle by heat will remain 8 kJ for the (Answer) same as as AUCO reversed process also. csscanned with CamScanner