Itinye iwu mbụ nke thermodynamics n'ọrụ na ụfọdụ usoro thermodynamic (Isobaric Isothermal Isochoric)

30 Itinye iwu mbụ nke thermodynamics n'ọrụ n'ụfọdụ usoro thermodynamic (Isobaric Isothermal Isochoric)

1. Grafụ dị n'okpuru na-egosi okirikiri thermodynamic nke gas na-ahụ. Ọrụ gas rụrụ na usoro ABCD bụ…

A maara:

Nrụgide 1 (P ₁ ) = 2 x 10 ⁵ Pa

Nrụgide 2 (P2 ₎ = 4 x 10 ⁵ Pa

Mpịakọta nke 1 (V ₁ ) = 1 m ³

Mpịakọta nke 2 (V ₂ ) = 3 m ³

Achọtara: Ọrụ gas rụrụ na usoro ABCD (W).

Ngwọta:

Ọrụ gas na-arụ hà nhata na mpaghara ABCD.

W = (P ₂ – P ₁ )(V ₂ – V ₁ )

W = (4 x 10 ⁵ – 2 x 10 ⁵ )(3 – 1)

W = (2 x 10 ⁵ )(2)

W = 4 x ¹⁰⁵ Joules

2. Ọrụ gas na-arụ na usoro ABC bụ…

A maara:

Nrụgide 1 (P1 ₎ = 3 x 10 ⁵ Pa

Nrụgide 2 (P2 ₎ = 6 x 10 ⁵ Pa

Mpịakọta nke 1 (V ₁ ) = 20 cm ³ = 20 x 10 ^-6 m ³

Mpịakọta nke 2 (V ₂ ) = 60 cm ³ = 60 x 10 ^-6 m ³

Achọsiri ike : Ọrụ gas rụrụ na usoro ABC

Ngwọta:

Ọrụ gas na-arụ = mpaghara ABC.

W = ½ (P ₂ – P ₁ )(V ₂ – V ₁ )

W = 1/2 (6 x 10 ⁵ – 3 x 10 ⁵ )(60 x 10 ^-6 – 20 x 10 ^-6 )

W = 1/2 (3 x 10 ⁵ )(40 x 10 ^-6 )

W = 1/2 (120 x 10 ^-1 Joules)

W = 1/2 (12 Joules)

W = Joule 6

3. Ihe osise PV maka gas dị n'ime akpa mechiri emechi nke egosiri na foto dị n'okpuru. A na-egosi ọrụ gas ahụ rụrụ na usoro ọ na-arụ.

ngwọta

Usoro AB na usoro DC bụ usoro isobaric (a na - eme ka nrụgide ahụ na-agbanwe agbanwe) . Usoro AD na usoro BC bụ usoro choric (olu anaghị agbanwe agbanwe ).

A rụrụ ọrụ ahụ site na gas mgbe gas ahụ gbasaa (usoro DC).

Lee nsogbu na ngwọta 9 metụtara Usoro Isobaric (Nrụgide Na-adịgide Adịgide):

Nsogbu 1:
A na-agbakọta gas 3.0 m³ na nrụgide na-adịgide adịgide ruo 2.0 m³. Ọ bụrụ na okpomọkụ mbụ bụ 300 K, kedu okpomọkụ ikpeazụ?

ngwọta:
Site na iji usoro nhazi maka usoro isobaric: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), anyị nwere ike idozi maka okpomọkụ ikpeazụ:

\[
\frac{3.0}{300} = \frac{2.0}{T_2} \pụtara T_2 = \frac{2.0 \times 300}{3.0} = 200\, \text{K}
\]

Nsogbu 2:
Gbakọọ ọrụ nke mole abụọ nke gas na-agbasa site na 1 lita ruo 3 lita na 2 atm.

ngwọta:
Iji usoro nhazi maka ọrụ emere na usoro isobaric: \( W = P \Delta V \):

\[
W = 2\, \text{atm} \times (3 – 1)\, \text{lita} = 4\, \text{atm}\cdot\text{lita}
\]

Nsogbu 3:
Kedu mgbanwe dị na ike dị n'ime mgbe a na-ekpo ọkụ mole 4 nke gas diatomic zuru oke na nrụgide na-adịgide adịgide site na 200 K ruo 300 K?

ngwọta:
Iji usoro maka mgbanwe na ike dị n'ime na nrụgide na-adịgide adịgide maka gas diatomic: \( \Delta U = nC_pdT \), ebe \( C_p = \frac{7}{2}R \):

\[
\Delta U = ugboro anọ \frac{7}{2} \ugboro 8.314 \ugboro (300 – 200) \ihe dịka 6990\, \text{J}
\]

Nsogbu 4:
Gbakọọ okpomọkụ agbakwunyere n'oge usoro isobaric mgbe moles abụọ nke gas monatomic gbasaa site na lita 5 ruo lita 10 na 400 K.

ngwọta:
Iji usoro maka mbufe okpomọkụ na usoro isobaric: \( Q = nC_pdT \), ebe \( C_p = \frac{5}{2}R \), na \( \frac{V_2}{T_2} = \frac{V_1}{T_1} \):

\[
Q = ugboro abụọ \frac{5}{2} \oge 8.314 \oge \ekpe(400 \oge \frac{10}{5} – 400\nri) = 3316\, \text{J}
\]

Nsogbu 5:
Chọpụta mgbanwe dị na enthalpy nke mole atọ nke gas triatomic nke a gbasaa site na lita 1 ruo lita 2 na okpomọkụ nke 200 K.

ngwọta:
Iji usoro maka mgbanwe na enthalpy maka usoro isobaric: \( \Delta H = nC_pdT \), ebe \( C_p = \frac{f}{2}R \) na \( f = 6 \):

\[
\Delta H = ugboro atọ \frac{6}{2} \oge 8.314 \oge \ekpe(200 \oge \frac{2}{1} – 200\nri) = 4989\, \text{J}
\]

Nsogbu 6:
Gbakọọ olu ikpeazụ nke moles abụọ nke gas na 300 K na lita 5 na mbụ mgbe a na-ekpo ọkụ ya ruo 500 K na nrụgide na-adịgide adịgide.

ngwọta:
Iji usoro maka usoro isobaric mee ihe:

\[
\frac{V_1}{T_1} = \frac{V_2}{T_2} \itinye V_2 = \frac{V_1 \times T_2}{T_1} = \frac{5 \times 500}{300} \approx 8.33\, \text{lita}
\]

Nsogbu 7:
Chọta ọrụ nke gas monatomic rụrụ mgbe a na-agbanye ya site na lita 6 ruo lita 3 na 2 atm.

ngwọta:
Iji usoro maka ọrụ emere na usoro isobaric:

\[
W = P \Delta V = ugboro abụọ (3 – 6) = -6\, \text{atm}\cdot\text{lita}
\]

Nsogbu 8:
Gas diatomic na-agbasa site na lita 3 ruo lita 6 na 300 K. Chọta mgbanwe na entropy.

ngwọta:
Iji usoro maka mgbanwe na entropy na usoro isobaric maka gas diatomic, ebe \(C_p = \frac{7}{2}R \):

\[
\Delta S = nC_p\ln\frac{T_2}{T_1} + nR\ln\frac{V_2}{V_1} = ugboro abụọ \frac{7}{2} \oge 8.314 \oge \ln\frac{300 \oge \frac{6}{3}}{300} + ugboro abụọ 8.314 \oge \ln\frac{6}{3} \ihe dị ka 34.76\, \text{J/K}
\]

Nsogbu 9:
Gbakọọ nnyefe okpomọkụ n'oge mkpakọ isobaric nke moles ise nke gas triatomic site na lita 10 ruo lita 5 na 500 K.

ngwọta:
Iji usoro maka mbufe okpomọkụ n'ime usoro isobaric, ebe \(C_p = \frac{f}{2}R \) na \(f = 6 \):

\[
Q = 5 \ugboro \frac{6}{2} \ugboro 8.314 \ugboro \ekpe(500 \ugboro \frac{5}{10} – 500\nri) = -12473\, \text{J}
\]

Nsogbu ndị a kwesịrị inye nkọwa zuru oke nke echiche dị iche iche metụtara usoro isobaric.

Lee nsogbu na ngwọta 9 metụtara Usoro Isothermal (Okpomọkụ Na-adịgide Adịgide):

 Nsogbu 1:
Nsogbu: Gbakọọ ọrụ nke mole abụọ nke gas zuru oke na-agbasa site na 1 lita ruo 2 lita na 300 K.

ngwọta:
Iji usoro maka ọrụ emere na usoro isothermal maka gas zuru oke:
\[ W = nRT\ln\frac{V_2}{V_1} \]

\[
W = ugboro abụọ 8.314 \ ugboro 300 \ ugboro \ln\frac{2}{1} \ ihe dịka 3454\, \text{J}
\]

Nsogbu 2:
Nsogbu: Chọta okpomọkụ e zigara mgbe a na-akpọnwụ mole atọ nke gas site na lita 4 ruo lita 2 na 400 K.

ngwọta:
Iji usoro maka mbufe okpomọkụ n'ime usoro isothermal: \( Q = W \):

\[
Q = ugboro atọ 8.314 \ ugboro 400 \ ugboro \ln\frac{2}{4} \ ihe dịka -3462\, \text{J}
\]

Nsogbu 3:
Chọpụta mgbanwe dị na entropy mgbe mole 4 nke gas na-enweta mgbasawanye isothermal site na 1 lita ruo 5 lita na 300 K.

ngwọta:
Iji usoro maka mgbanwe na entropy na usoro isothermal:

\[
\Delta S = nR\ln\frac{V_2}{V_1} = ugboro anọ 8.314 \oge \ln\frac{5}{1} \ihe dị ka 46.15\, \text{J/K}
\]

Nsogbu 4:
Gbakọọ ọrụ e mere mgbe a gbakọrọ otu mole nke gas zuru oke site na lita 6 ruo lita 3 na 200 K.

ngwọta:
Iji usoro nhazi maka ọrụ emere na usoro isothermal:

\[
W = 1 \ugboro 8.314 \ugboro 200 \ugboro \ln\frac{3}{6} \ugboro -575\, \ederede{J}
\]

Nsogbu 5:
Chọpụta mgbanwe dị na ike dị n'ime maka mole atọ nke gas n'oge mgbasawanye isothermal site na lita 2 ruo lita 6 na okpomọkụ na-agbanwe agbanwe.

ngwọta:
Maka usoro isothermal nke gas zuru oke, mgbanwe nke ike dị n'ime bụ efu:

\[
\Delta U = 0\, \ederede{J}
\]

Nsogbu 6:
Gbakọọ mbufe okpomọkụ mgbe agbatịchara mole 5 nke gas site na lita 3 ruo lita 6 na 250 K.

ngwọta:
Iji usoro maka mbufe okpomọkụ na usoro isothermal:

\[
Q = 5 \ugboro 8.314 \ugboro 250 \ugboro \ln\frac{6}{3} \ihe dịka 2879\, \text{J}
\]

Nsogbu 7:
Kedu ọrụ nke moles abụọ nke gas na-arụ n'oge nrụgide isothermal site na lita 4 ruo lita 2 na 150 K?

ngwọta:
Iji usoro nhazi maka ọrụ emere na usoro isothermal:

\[
W = 2 \ugboro 8.314 \ugboro 150 \ugboro \ln\frac{2}{4} \ugboro -1151\, \ederede{J}
\]

Nsogbu 8:
Chọta mgbanwe dị na entropy mgbe a na-akpọnwụ mole atọ nke gas site na lita 5 ruo lita 1 na 500 K.

ngwọta:
Iji usoro maka mgbanwe na entropy na usoro isothermal:

\[
\Delta S = ugboro atọ 8.314 \oge \ln\frac{1}{5} \ihe dị ka -34.77\, \text{J/K}
\]

Nsogbu 9:
Chọpụta ọrụ nke 4 moles nke gas zuru oke na-arụ, gbasaa site na lita 2 ruo lita 8 na 100 K.

ngwọta:
Iji usoro nhazi maka ọrụ emere na usoro isothermal:

\[
W = ugboro abụọ 8.314 \ ugboro 100 \ ugboro \ln\frac{4}{2} \ ihe dịka 2304\, \text{J}
\]

Nsogbu ndị a na-ekpuchi echiche dị iche iche metụtara usoro isothermal, dịka ọrụ emere, nnyefe okpomọkụ, na mgbanwe na entropy.

Lee nsogbu na ngwọta 9 metụtara Usoro Isochoric (Mpịakọta Na-agbanwe agbanwe):

Nsogbu 1:
Gbakọọ mgbanwe dị na ike dị n'ime maka moles atọ nke gas kacha mma monatomic mgbe a mụbara okpomọkụ site na 200 K ruo 400 K na olu na-agbanweghi agbanwe.

ngwọta:
Iji usoro maka mgbanwe na ike dị n'ime na olu na-agbanwe agbanwe: \( \Delta U = nC_v\Delta T \), ebe \( C_v = \frac{3}{2}R \):

\[
\Delta U = ugboro anọ \frac{3}{2} \ugboro 8.314 \ugboro (400 – 200) \ihe dịka 3741\, \text{J}
\]

Nsogbu 2:
Chọpụta nnyefe okpomọkụ maka moles abụọ nke gas diatomic mgbe okpomọkụ ahụ belatara site na 300 K ruo 200 K na olu na-agbanweghi agbanwe.

ngwọta:
Iji usoro maka mbufe okpomọkụ na olu na-agbanwe agbanwe: \( Q = \Delta U = nC_v\Delta T \), ebe \( C_v = \frac{5}{2}R \):

\[
Q = ugboro abụọ \frac{5}{2} \ugboro 8.314 \ugboro (200 - 300) \ihe dịka -4157\, \text{J}
\]

Nsogbu 3:
Gbakọọ mgbanwe dị na entropy maka moles anọ nke gas triatomic mgbe okpomọkụ na-arị elu site na 100 K ruo 300 K na olu na-agbanwe agbanwe.

ngwọta:
Iji usoro maka mgbanwe na entropy na olu na-agbanwe agbanwe, ebe \(C_v = \frac{f}{2}R \) na \(f = 6 \):

\[
\Delta S = nC_v\ln\frac{T_2}{T_1} = ugboro anọ \frac{6}{2} \oge 8.314 \oge \ln\frac{300}{100} \ihe dị ka 115.36\, \text{J/K}
\]

Nsogbu 4:
Kedu ọrụ gas na-arụ n'oge usoro isochoric?

ngwọta:
Ebe ọ bụ na olu ahụ na-adịgide adịgide n'oge usoro isochoric, ọ dịghị ọrụ emere:

\[
W = 0\, \ederede{J}
\]

Nsogbu 5:
Chọpụta nnyefe okpomọkụ maka moles ise nke gas kacha mma monatomic mgbe a jụrụ ya oyi site na 500 K ruo 300 K na olu na-agbanweghi agbanwe.

ngwọta:
Site na iji usoro maka mbufe okpomọkụ na olu na-agbanwe agbanwe, ebe \(C_v = \frac{3}{2}R \):

\[
Q = ugboro abụọ \frac{3}{5} \ugboro 8.314 \ugboro (300 - 500) \ihe dịka -6232\, \text{J}
\]

Nsogbu 6:
Gbakọọ mgbanwe dị na ike dị n'ime maka 1 mole nke gas diatomic mgbe a mụbara okpomọkụ site na 150 K ruo 250 K na olu na-agbanweghi agbanwe.

ngwọta:
Iji usoro maka mgbanwe na ike dị n'ime na olu na-agbanwe agbanwe, ebe \(C_v = \frac{5}{2}R \):

\[
\Delta U = ugboro anọ \frac{5}{2} \ugboro 8.314 \ugboro (250 – 150) \ihe dịka 2079\, \text{J}
\]

Nsogbu 7:
Chọpụta mgbanwe dị na entropy maka moles atọ nke gas monatomic mgbe okpomọkụ belatara site na 600 K ruo 300 K na olu na-agbanweghi agbanwe.

ngwọta:
Iji usoro maka mgbanwe na entropy na olu na-agbanwe agbanwe, ebe \(C_v = \frac{3}{2}R \):

\[
\Delta S = ugboro atọ \frac{3}{2} \oge 8.314 \oge \ln\frac{300}{600} \ihe dị ka -34.59\, \text{J/K}
\]

Nsogbu 8:
Kedu ihe bụ mbufe okpomọkụ maka moles abụọ nke gas triatomic mgbe a mụbara okpomọkụ site na 200 K ruo 400 K na olu na-agbanwe agbanwe?

ngwọta:
Site na iji usoro maka mbufe okpomọkụ na olu na-agbanwe agbanwe, ebe \(C_v = \frac{6}{2}R \):

\[
Q = ugboro abụọ \frac{6}{2} \ugboro 8.314 \ugboro (400 - 200) \ihe dịka 4986\, \text{J}
\]

Nsogbu 9:
Gbakọọ mgbanwe dị na ike dị n'ime maka moles anọ nke gas kacha mma nke monatomic mgbe a na-ekpo ọkụ ya site na 250 K ruo 350 K na olu na-agbanweghi agbanwe.

ngwọta:
Iji usoro maka mgbanwe na ike dị n'ime na olu na-agbanwe agbanwe, ebe \(C_v = \frac{3}{2}R \):

\[
\Delta U = ugboro anọ \frac{3}{2} \ugboro 8.314 \ugboro (350 – 250) \ihe dịka 4986\, \text{J}
\]

Nsogbu ndị a na-ekpuchi akụkụ dị iche iche nke usoro isochoric, dịka nnyefe okpomọkụ, mgbanwe na ike dị n'ime, na entropy, maka ụdị gas dị iche iche.