Question

internal energy change when a monoatomic ideal gas is compressed reversibly from 16 L to 2L at 300K?​

Answer 1

change in internal energy of one mole of monoatomic ideal gas is 11250 J

we have to find the internal energy change when a monoatomic ideal gas is compressed reversibly from 16L to 2L at 300K.

using formula, $TV^{\gamma-1}=\textbf{constant}$

⇒$T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}$

here, T₁ = 300K, V₁ = 16L, T₂ = ?, γ = 5/3 and V₂ = 2L

⇒$(300)(16)^{5/3-1}=T_2(2)^{5/3-1}$

⇒300 × (16)^2/3 = T₂ × (2)^2/3

⇒T₂ = 300 × (8)^2/3 = 300 × 4 = 1200 K

now change in internal energy , ∆U = nCv∆T

= 1 × 3R/2 × (1200 - 300)

= 3R/2 × 900

= 3 × 25/3 × 450 [ R = 25/3 J/mol/K ]

= 25 × 450

= 11250 J

therefore change in internal energy of one mole of monoatomic ideal gas is 11250 J

Answer 2

Answer:

change in internal energy of one mole of monoatomic ideal gas is 11250 J

we have to find the internal energy change when a monoatomic ideal gas is compressed reversibly from 16L to 2L at 300K.

using formula,

⇒

here, T₁ = 300K, V₁ = 16L, T₂ = ?, γ = 5/3 and V₂ = 2L

⇒

⇒300 × (16)^2/3 = T₂ × (2)^2/3

⇒T₂ = 300 × (8)^2/3 = 300 × 4 = 1200 K

now change in internal energy , ∆U = nCv∆T

= 1 × 3R/2 × (1200 - 300)

= 3R/2 × 900

= 3 × 25/3 × 450 [ R = 25/3 J/mol/K ]

= 25 × 450

= 11250 J

therefore change in internal energy of one mole of monoatomic ideal gas is 11250 J