n = 3.36 mol of Hydrogen gas is initially at T = 348 K temperature and pi = 2.98
ID: 1511900 • Letter: N
Question
n = 3.36 mol of Hydrogen gas is initially at T = 348 K temperature and pi = 2.98×105 Pa pressure. The gas is then reversibly and isothermally compressed until its pressure reaches pf = 8.10×105 Pa. Volume of the gas at the end of the compression process is1.20×10-2 m^3.
How much work did the external force perform?
How much heat did the gas emit?
How much entropy did the gas emit?
What would be the temperature of the gas, if the gas was allowed to adiabatically expand back to its original pressure?
Explanation / Answer
from the ideal gas equation
PiVi = Pf Vf
Vf = Pi Vi/Pf.
=2.98×10^5 Pa ( Vi)/( 8.10×10^5 Pa
=0.367 Vi
work done is
W = 2.302 nRT log(Pi/Pf)
= 2.302 ( 3.36) ( 8.314)(348) log(2.98×10^5 Pa/8.10×10^5)
=-9718.34 J
(b)
heat emit is
Q = -W= 9718.34 J
(c)
dels = Q/T = 9718.34 J/348 = 27.92 J/K
(d)
the relation between temperature and volume
Tf = Ti ( Vf/Vi) ^gama-1
=348 ( 0.367 Vi/Vi) ^1.4-1
=233 K
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