Question

4. One mole of monoatomic ideal gas, initially at 27 oC and 1 bar, is heated and allowed to expand reversibly against constant pressure of 1 bar until the final temperature is 127 °C. 4.1 What are the initial (Vi) and final (V2) volumes of the gas? 4.2 Calculate the work (w) that the gas does during this expansion. 4.3 Calculate the internal energy change (AU) of this expansion process 4.4 Calculate the enthalpy change (AH) of this expansion process.

Answer 1

4.1

T₁ = initial temperature = 27 ^oC = 27 + 273 = 300 K

T₂ = final temperature = 127 ^oC = 127 + 273 = 400 K

P = pressure = 1 bar = 10⁵ pa

n = number of moles = 1

V₁ = initial volume

Using the ideal gas equation

P V₁ = n R T₁

(10⁵) V₁ = (1) (8.314) (300)

V₁ = 0.025 m³

Using the ideal gas equation

P V₂ = n R T₂

(10⁵) V₂ = (1) (8.314) (400)

V₂ = 0.033 m³

4.2

work done is given as

W = P (V₂ - V₁)

W = (10⁵) (0.033 0.025)

W = 82.5 J

4.3

internal energy change is given as

$\Delta$U = n C_v (T₂ - T₁)

$\Delta$U = (1) (12.5) (400- 300)

$\Delta$U = 1250 J

4.4 )

Enthalpy change is given as

$\Delta$H = n C_p (T₂ - T₁)

$\Delta$H = (1) (20.8) (400- 300)

$\Delta$H = 2080 J