A sample of a monatomic ideal gas is taken through the cyclic process abca shown
ID: 1483158 • Letter: A
Question
A sample of a monatomic ideal gas is taken through the cyclic process abca shown in the figure below. The values along the pressure axis are pb = 7.50 kPa and pac = 2.50 kPa. The values along the volume axis are Va = 1.00 m3 and Vbc = 3.00 m3. The temperature at state a is Ta = 200 K. (a) How many moles of gas are in the sample? (b) What is the temperature of the gas at point b? (c) What is the temperature of the gas at point c? (d) What is the net energy added to the gas as heat along each step in the cycle and over the entire cycle?
Explanation / Answer
using ideal gas equation Pa*Va = n*R*Ta
2.5*1000*1 = n*8.314*200
no.of moles are n = 2500/(8.314*200) = 1.5 moles
B) Pa*Va/Ta = Pb*Vb/Tb
2.5*1/200 = 7.5*3/Tb
Tb = 1800 K
C) Pb/Tb = Pc/Tc
Tc = 7.5/1800 = 2.5/Tc
Tc = 600 K
d) from a to c
Q1 = P*dV 2.5*1000*2 = 5000 J
from c to b Q2 = P*dV = P*0 = 0 J
from b to a
Q3 = 0 J
total energy added is 0.5*2*5000 = 5000 J