Shows a thermodynamic process followed by 120 mg of helium. a. Determine the pre

Question

Shows a thermodynamic process followed by 120 mg of helium. a. Determine the pressure (in atm), temperature (in degree C), and volume (in cm^3) of the gas at points 1, 2, and 3. Put your results in a table for easy reading. b. How much work is done on the gas during each of the three segments? c. How much heat energy is transferred to or from the gas during each of the three segments? a. What compression ratio V_max/V_min will raise the air temperature from 20 degree C to 1000 degree C in an adiabatic process? b. What pressure ratio P_max/P_min does this process have?

Explanation / Answer

a )

helium is monoatomic gas

then n = 120 X 10-3 / 4

n = 0.03 mol

changing transition 1 ----> 2

P1 = n R T1 / V1

P1 = 0.03 X 8.314 X 406 / ( 1 / 1000 )

P1 = 1.013 X 105 Pa or 1 atm

in isochoric process

T2 = P2 T1 / P1

T2 = 5 T1

= 5 X 460

= 2300 K

sameway transition 2 ---> 3

V3 = P2 V1 / P1

= 5 V1

= 5 X 10-3 m3

b )

in transition 1 ----> 2

W12 = 0

transition 2 ----> 3 is isothermic

then W2----->3 = P2 V2 ln ( V3 / V2 )

= 5 X 105 X 10-3X ln ( 5 / 1 )

= 804.71 J

transition 2 ----> 3 is isobaric

W3----->1 = P3 ( V1 - V3 )

= 1.013 X 105 X ( 1 - 5 ) X 10-3

= - 405.2 J

c )

Q1---->2 = n CV dT

= 3/2 n R ( T2 - T1 )

= 3/2 ( P2 V2 - P1 V1 )

= 3/2 X ( 5 X 105 X 10-3 - 1 X 105 X 10-3 )

= 609 J

Q2---->3 = W2----->3 = 814.7 J

Q3----->1 = n CPdT

= 5/2 n R ( T1 - T3 )

= 3/2 ( P1 V1 - P3 V3 )

= 5/2 X ( 105 X 10-3 - 5 X 105 X 10-3 )

= - 1013 J

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