30 Tšebeliso ea molao oa pele oa thermodynamics lits'ebetsong tse ling tsa thermodynamic (Isobaric Isothermal Isochoric)
1. Kerafo e ka tlase e bonts'a potoloho ea thermodynamic e bonoang ke khase. Mosebetsi o etsoang ke khase ts'ebetsong ea ABCD ke ...
Tse tsejoang:
Khatello 1 (P 1 ) = 2 x 10 5 Pa
Khatello ea 2 (P 2 ) = 4 x 10 5 Pa
Moqolo oa 1 (V 1 ) = 1 m 3
Moqolo oa 2 (V 2 ) = 3 m 3
Ho batloa: Mosebetsi o etsoang ke khase ts'ebetsong ea ABCD (W).
Tharollo:
Mosebetsi o etsoang ke khase o lekana le sebaka sa 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 10 5 Joule
2. Mosebetsi o etsoang ke khase ts'ebetsong ea ABC ke…
Tse tsejoang:
Khatello ea 1 (P 1 ) = 3 x 10 5 Pa
Khatello ea 2 (P 2 ) = 6 x 10 5 Pa
Moqolo oa 1 (V 1 ) = 20 cm 3 = 20 x 10 -6 m 3
Moqolo oa 2 (V 2 ) = 60 cm 3 = 60 x 10 -6 m 3
Ho batloa : Mosebetsi o entsoeng ke khase ts'ebetsong ea ABC
Tharollo:
Mosebetsi o etsoang ke khase = sebaka sa 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 Joule)
W = 1/2 (Lijoule tse 12)
W = 6 Joule
3. Setšoantšo sa PV bakeng sa khase ka har'a setshelo se koetsoeng se bontšitsoeng setšoantšong se ka tlase. Mosebetsi o etsoang ke khase o bontšoa ts'ebetsong efe.
tharollo
Ts'ebetso ea AB le ts'ebetso ea DC ke lits'ebetso tsa isobaric (khatello e lula e tsitsitse) . Ts'ebetso ea AD le ts'ebetso ea BC ke lits'ebetso tsa choric (bophahamo ha bo fetohe).
Mosebetsi o entsoe ka khase ha khase e atoloha (tshebetso ya DC).
Mona ke mathata le litharollo tse 9 tse amanang le Ts'ebetso ea Isobaric (Khatello e sa Feleng):
Bothata ba 1:
Khase ea 3.0 m³ ka khatello e sa fetoheng e hatelloa ho 2.0 m³. Haeba mocheso oa pele e le 300 K, mocheso oa ho qetela ke ofe?
tharollo:
Re sebelisa equation bakeng sa ts'ebetso ea isobaric: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), re ka rarolla mocheso oa ho qetela:
\[
\frac{3.0}{300} = \frac{2.0}{T_2} \e bolela T_2 = \frac{2.0 \times 300}{3.0} = 200\, \text{K}
\]
Bothata ba 2:
Bala mosebetsi o entsoeng ke limole tse 2 tsa khase tse ntseng li atoloha ka isobarically ho tloha lithareng tse 1 ho isa ho tse 3 ho 2 atm.
tharollo:
Ho sebedisa equation bakeng sa mosebetsi o entsweng tshebetsong ya isobaric: \( W = P \Delta V \):
\[
W = 2\, \text{atm} \times (3 - 1)\, \text{liters} = 4\, \text{atm}\cdot\text{liters}
\]
Bothata ba 3:
Phetoho ea matla a ka hare ke efe ha limole tse 4 tsa khase e ntle ea diatomic li futhumatsoa ka khatello e sa khaotseng ho tloha ho 200 K ho isa ho 300 K?
tharollo:
Ho sebedisa equation bakeng sa phetoho ya matla a ka hare kgatellong e sa fetoheng bakeng sa kgase ya diatomic: \( \Delta U = nC_pdT \), moo \( C_p = \frac{7}{2}R \):
\[
\Delta U = 4 \makgetlo \frac{7}{2} \makgetlo a 8.314 \makgetlo (300 - 200) \hoo e ka bang 6990\, \mongolo{J}
\]
Bothata ba 4:
Bala mocheso o ekelitsoeng nakong ea ts'ebetso ea isobaric ha li-mole tse 2 tsa khase ea monatomic li atoloha ho tloha ho lilithara tse 5 ho isa ho lilithara tse 10 ho 400 K.
tharollo:
Ho sebedisa equation bakeng sa phetiso ya mocheso tshebetsong ya isobaric: \( Q = nC_pdT \), moo \( C_p = \frac{5}{2}R \), le \( \frac{V_2}{T_2} = \frac{V_1}{T_1} \):
\[
Q = 2 \makgetlo \frac{5}{2} \makgetlo a 8.314 \makgetlo \left(400 \makgetlo \frac{10}{5} – 400\left) = 3316\, \text{J}
\]
Bothata ba 5:
Fumana phetoho ho enthalpy ea limole tse 3 tsa khase ea triatomic e atolositsoeng ho tloha ho litara e le 1 ho isa ho lilithara tse 2 mochesong oa 200 K.
tharollo:
Ho sebedisa foromo ya phetoho ho enthalpy bakeng sa tshebetso ya isobaric: \( \Delta H = nC_pdT \), moo \( C_p = \frac{f}{2}R \) le \( f = 6 \):
\[
\Delta H = 3 \makgetlo \frac{6}{2} \makgetlo a 8.314 \makgetlo \left(200 \makgetlo \frac{2}{1} – 200\left) = 4989\, \text{J}
\]
Bothata ba 6:
Bala bophahamo ba ho qetela ba limole tse 2 tsa khase ho 300 K le lilithara tse 5 qalong ha e futhumatsoa ho 500 K ka khatello e sa fetoheng.
tharollo:
Ho sebelisa equation bakeng sa ts'ebetso ea isobaric:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2} \e bolela V_2 = \frac{V_1 \times T_2}{T_1} = \frac{5 \times 500}{300} \hoo e ka bang 8.33\, \text{liters}
\]
Bothata ba 7:
Fumana mosebetsi o etsoang ke khase ea monatomic ha e hatelloa ho tloha lilithareng tse 6 ho isa ho tse 3 ka 2 atm.
tharollo:
Ho sebelisa equation bakeng sa mosebetsi o entsoeng ts'ebetsong ea isobaric:
\[
W = P \Delta V = 2 \makgetlo (3 - 6) = -6\, \text{atm}\cdot\text{liters}
\]
Bothata ba 8:
Khase ea diatomic e feta katolosong ea isobaric ho tloha ho lilithara tse 3 ho isa ho lilithara tse 6 mochesong oa 300 K. Fumana phetoho ho entropy.
tharollo:
Ho sebedisa equation bakeng sa phetoho ya entropy tshebetsong ya isobaric bakeng sa kgase ya diatomic, moo \( C_p = \frac{7}{2}R \):
\[
\Delta S = nC_p\ln\frac{T_2}{T_1} + nR\ln\frac{V_2}{V_1} = 2 \times \frac{7}{2} \times 8.314 \times \ln\frac{300 \times \frac{6}{3}}{300} + 2 \times 8.314 \times \ln\frac{6}{3} \hoo e ka bang 34.76\, \text{J/K}
\]
Bothata ba 9:
Bala phetiso ea mocheso nakong ea khatello ea isobaric ea li-mole tse 5 tsa khase ea triatomic ho tloha ho lilithara tse 10 ho isa ho lilithara tse 5 ho 500 K.
tharollo:
Ho sebedisa equation bakeng sa phetiso ya mocheso tshebetsong ya isobaric, moo \( C_p = \frac{f}{2}R \) le \( f = 6 \):
\[
Q = 5 \makgetlo \frac{6}{2} \makgetlo a 8.314 \makgetlo \left(500 \makgetlo \frac{5}{10} – 500\left) = -12473\, \text{J}
\]
Mathata ana a lokela ho fana ka kakaretso e felletseng ea likhopolo tse fapaneng tse amanang le ts'ebetso ea isobaric.
Mona ke mathata le litharollo tse 9 tse amanang le Ts'ebetso ea Isothermal (Mocheso o sa Feleng):
Bothata ba 1:
Bothata: Bala mosebetsi o entsoeng ke limole tse 2 tsa khase e ntle e ntseng e hola ka mokhoa o sa fetoheng ho tloha ho litara e le 1 ho isa ho lilithara tse 2 ka mocheso oa 300 K.
tharollo:
Ho sebelisa equation bakeng sa mosebetsi o entsoeng ts'ebetsong ea isothermal bakeng sa khase e loketseng:
\[ W = nRT\ln\frac{V_2}{V_1} \]
\[
W = 2 \ka makhetlo a 8.314 \ka makhetlo a 300 \ka makhetlo \ln\frac{2}{1} \ka hoo e ka bang 3454\, \mongolo{J}
\]
Bothata ba 2:
Bothata: Fumana mocheso o fetiselitsoeng ha limole tse 3 tsa khase li hatelloa ka isothermally ho tloha lilithareng tse 4 ho isa ho tse 2 ka mocheso oa 400 K.
tharollo:
Ho sebedisa equation bakeng sa phetiso ya mocheso tshebetsong ya isothermal: \( Q = W \):
\[
Q = 3 \makgetlo a 8.314 \makgetlo a 400 \makgetlo \ln\frac{2}{4} \hoo e ka bang -3462\, \mongolo{J}
\]
Bothata ba 3:
Fumana phetoho ho entropy ha limole tse 4 tsa khase li feta katolosong ea isothermal ho tloha lithareng tse 1 ho isa ho tse 5 ho 300 K.
tharollo:
Ho sebelisa equation bakeng sa phetoho ea entropy ts'ebetsong ea isothermal:
\[
\Delta S = nR\ln\frac{V_2}{V_1} = 4 \ka makhetlo a 8.314 \ka makhetlo \ln\frac{5}{1} \hoo e ka bang 46.15\, \mongolo{J/K}
\]
Bothata ba 4:
Bala mosebetsi o entsoeng ha mole e le 'ngoe ea khase e loketseng e hatelloa ka isothermally ho tloha lilithareng tse 6 ho isa ho tse 3 ho 200 K.
tharollo:
Ho sebelisa equation bakeng sa mosebetsi o etsoang ts'ebetsong ea isothermal:
\[
W = 1 \ka makhetlo a 8.314 \ka makhetlo a 200 \ka makhetlo \ln\frac{3}{6} \ka -575\, \mongolo{J}
\]
Bothata ba 5:
Fumana phetoho ea matla a ka hare bakeng sa limolek'hule tse 3 tsa khase nakong ea katoloso ea isothermal ho tloha ho lilithara tse 2 ho isa ho tse 6 mochesong o sa fetoheng.
tharollo:
Bakeng sa ts'ebetso ea isothermal ea khase e loketseng, phetoho ea matla a ka hare ke lefela:
\[
\Delta U = 0\, \mongolo{J}
\]
Bothata ba 6:
Bala phetiso ea mocheso ha limole tse 5 tsa khase li atolosoa ka isothermally ho tloha lilithareng tse 3 ho isa ho tse 6 ho 250 K.
tharollo:
Ho sebelisa equation bakeng sa phetiso ea mocheso ts'ebetsong ea isothermal:
\[
Q = 5 \ka makhetlo a 8.314 \ka makhetlo a 250 \ka makhetlo \ln\frac{6}{3} \hoo e ka bang 2879\, \mongolo{J}
\]
Bothata ba 7:
Mosebetsi o etsoang ke limole tse 2 tsa khase nakong ea khatello ea isothermal ho tloha lilithareng tse 4 ho isa ho tse 2 ka mocheso oa 150 K ke ofe?
tharollo:
Ho sebelisa equation bakeng sa mosebetsi o etsoang ts'ebetsong ea isothermal:
\[
W = 2 \ka makhetlo a 8.314 \ka makhetlo a 150 \ka makhetlo \ln\frac{2}{4} \ka -1151\, \mongolo{J}
\]
Bothata ba 8:
Fumana phetoho ho entropy ha limole tse 3 tsa khase li hatelloa ka isothermally ho tloha lilithara tse 5 ho isa lithara tse 1 ho 500 K.
tharollo:
Ho sebelisa equation bakeng sa phetoho ea entropy ts'ebetsong ea isothermal:
\[
\Delta S = 3 \ka makhetlo a 8.314 \ka makhetlo \ln\frac{1}{5} \hoo e ka bang -34.77\, \mongolo{J/K}
\]
Bothata ba 9:
Fumana mosebetsi o entsoeng ke limole tse 4 tsa khase e ntle e ntseng e hola ka mokhoa o sa fetoheng ho tloha ho lilithara tse 2 ho isa ho tse 8 ka matla a 100 K.
tharollo:
Ho sebelisa equation bakeng sa mosebetsi o etsoang ts'ebetsong ea isothermal:
\[
W = 4 \ka makhetlo a 8.314 \ka makhetlo a 100 \ka makhetlo \ln\frac{8}{2} \ka hoo e ka bang 2304\, \mongolo{J}
\]
Mathata ana a akaretsa mehopolo e fapaneng e amanang le ts'ebetso ea isothermal, joalo ka mosebetsi o entsoeng, phetisetso ea mocheso, le phetoho ea entropy.
Mona ke mathata le litharollo tse 9 tse amanang le Ts'ebetso ea Isochoric (Molumo o sa Feleng):
Bothata ba 1:
Bala phetoho ea matla a ka hare bakeng sa limole tse 3 tsa khase e ntle ea monatomic ha mocheso o eketsehile ho tloha ho 200 K ho isa ho 400 K ka molumo o sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetoho ya eneji ya ka hare ka bophahamo ba modumo bo sa fetoheng: \( \Delta U = nC_v\Delta T \), moo \( C_v = \frac{3}{2}R \):
\[
\Delta U = 3 \makgetlo \frac{3}{2} \makgetlo a 8.314 \makgetlo (400 - 200) \hoo e ka bang 3741\, \mongolo{J}
\]
Bothata ba 2:
Fumana phetiso ea mocheso bakeng sa limole tse 2 tsa khase ea diatomic ha mocheso o theohile ho tloha ho 300 K ho isa ho 200 K ka bophahamo bo sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetiso ya mocheso ka bophahamo bo sa fetoheng: \( Q = \Delta U = nC_v\Delta T \), moo \( C_v = \frac{5}{2}R \):
\[
Q = 2 \makgetlo \frac{5}{2} \makgetlo a 8.314 \makgetlo (200 - 300) \hoo e ka bang -4157\, \mongolo{J}
\]
Bothata ba 3:
Bala phetoho ho entropy bakeng sa limole tse 4 tsa khase ea triatomic ha mocheso o eketseha ho tloha ho 100 K ho isa ho 300 K ka bophahamo bo sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetoho ya entropy ka bophahamo ba modumo bo sa fetoheng, moo \( C_v = \frac{f}{2}R \) le \( f = 6 \):
\[
\Delta S = nC_v\ln\frac{T_2}{T_1} = 4 \times \frac{6}{2} \times 8.314 \times \ln\frac{300}{100} \hoo e ka bang 115.36\, \text{J/K}
\]
Bothata ba 4:
Mosebetsi o etsoang ke khase nakong ea ts'ebetso ea isochoric ke ofe?
tharollo:
Kaha molumo o tsitsitse nakong ea ts'ebetso ea isochoric, ha ho mosebetsi o etsoang:
\[
W = 0, \mongolo{J}
\]
Bothata ba 5:
Fumana phetiso ea mocheso bakeng sa li-mole tse 5 tsa khase e ntle ea monatomic ha e pholisitsoe ho tloha ho 500 K ho isa ho 300 K ka molumo o sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetiso ya mocheso ka bophahamo ba modumo bo sa fetoheng, moo \( C_v = \frac{3}{2}R \):
\[
Q = 5 \makgetlo \frac{3}{2} \makgetlo a 8.314 \makgetlo (300 - 500) \hoo e ka bang -6232\, \mongolo{J}
\]
Bothata ba 6:
Bala phetoho ea matla a ka hare bakeng sa mole e le 'ngoe ea khase ea diatomic ha mocheso o eketsehile ho tloha ho 150 K ho ea ho 250 K ka molumo o sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetoho ya eneji ya ka hare ka bophahamo ba modumo bo sa fetoheng, moo \( C_v = \frac{5}{2}R \):
\[
\Delta U = 1 \makgetlo \frac{5}{2} \makgetlo a 8.314 \makgetlo (250 - 150) \hoo e ka bang 2079\, \mongolo{J}
\]
Bothata ba 7:
Fumana phetoho ho entropy bakeng sa limole tse 3 tsa khase ea monatomic ha mocheso o theoha ho tloha ho 600 K ho ea ho 300 K ka bophahamo bo sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetoho ya entropy ka bophahamo ba modumo bo sa fetoheng, moo \( C_v = \frac{3}{2}R \):
\[
\Delta S = 3 \makgetlo \frac{3}{2} \makgetlo 8.314 \makgetlo \ln\frac{300}{600} \hoo e ka bang -34.59\, \mongolo{J/K}
\]
Bothata ba 8:
Phetiso ea mocheso bakeng sa limole tse 2 tsa khase ea triatomic ke eng ha mocheso o eketsehile ho tloha ho 200 K ho isa ho 400 K ka molumo o sa fetoheng?
tharollo:
Ho sebedisa equation bakeng sa phetiso ya mocheso ka bophahamo ba modumo bo sa fetoheng, moo \( C_v = \frac{6}{2}R \):
\[
Q = 2 \makgetlo \frac{6}{2} \makgetlo a 8.314 \makgetlo (400 - 200) \hoo e ka bang 4986\, \mongolo{J}
\]
Bothata ba 9:
Bala phetoho ea matla a ka hare bakeng sa limole tse 4 tsa khase e ntle ea monatomic ha e futhumatsoa ho tloha ho 250 K ho isa ho 350 K ka molumo o sa fetoheng.
tharollo:
Ho sebedisa equation bakeng sa phetoho ya eneji ya ka hare ka bophahamo ba modumo bo sa fetoheng, moo \( C_v = \frac{3}{2}R \):
\[
\Delta U = 4 \makgetlo \frac{3}{2} \makgetlo a 8.314 \makgetlo (350 - 250) \hoo e ka bang 4986\, \mongolo{J}
\]
Mathata ana a akaretsa likarolo tse fapaneng tsa ts'ebetso ea isochoric, joalo ka phetiso ea mocheso, liphetoho matla a ka hare, le entropy, bakeng sa mefuta e fapaneng ea likhase.
