Surroundings 74114

In a cylinder with a piston, there is nitrogen N2 with a volume of 5 liters, a temperature of 25 degrees Celsius, and a pressure of 200 kPa.
We very slowly compress the gas in the cylinder to half its volume while its temperature does not change.
Determine the resulting gas pressure and the heat that passes through the walls of the cylinder to the surroundings.

Correct answer:

p2 =  400 kPa
E =  693.1472 J

Step-by-step explanation:

V1=5 l m3=5:1000  m3=0.005 m3 T=25°CK=25+273.16 K=298.16 K p1=200 kPa  V2=V1/2=2001/2=200 21=4001=0.0025 m3   tp   V  = const p1 V1 = p2 V2  p2=p1 V2V1=200 40012001=400 kPa
R=8.314462618153248.3145 J/K/mol M=2.14 1030.0021 kg/mol  P1=p1 1000=200 1000=200000 Pa  m=R TP1 V1 M=8.3145 298.16200000 0.005 0.00210.0009 kg  n=m/M=0.0009/0.00210.4034 mol  E=n R T ln(V2/V1)=0.4034 8.3145 298.16 ln(0.0025/0.005)=693.1472 J

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