0.20 moles of Helium gas that initially occupies a volume of 4.0L under a total

Question

0.20 moles of Helium gas that initially occupies a volume of 4.0L under a total pressure of 1.0x10^5 Pa, subsequently undergoes an isobaric expansion to 5.0L followed by an isothermal expansion to 8.0L.

a.) What is the specific heat at constant volume?
b.) What is the specific heat at constant temperature?
c.) What is the initial temperature of the gas?
d.) What are the pressure and temperature of the gas at the end of the isobaric expansion?
e.) What are the pressure, and temperature of the gas after the isothermal expansion?

Explanation / Answer

(a) For monoatomic gases like Helium, specific heat at constant volume Cv = 12.5 J/mol-K

(b) For monoatomic gases like Helium, specific heat at constant pressure Cp = 20.8 J/mol-K

(c) Using p1V1 = nRT1, (1*105)*(4*10-3) = 0.2*8.314*T1

So, T1 = 240.6 K

(d) For isobaric expansion, P is constant and V is proportional to T.

So, P2 = P1 = 1*105 Pa and T2 = (V2/V1)*T1 = 5/4*240.6 = 300.7 K

(e) For isothermal expansion, P is inversely proportional to V and T remains constant.

So, T3 = T2 = 300.7 K and

P2V2 = P3V3

So, 1*105 * 5 = P3 * 8

So, P3 = 62500 Pa

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