30 Ukusetshenziswa komthetho wokuqala we-thermodynamics kwezinye izinqubo ze-thermodynamic (i-Isobaric Isothermal Isochoric)
1. Igrafu engezansi ikhombisa umjikelezo we-thermodynamic obonwa yigesi. Umsebenzi owenziwe yigesi enqubweni i-ABCD …
Kwaziwa:
Ingcindezi 1 (P 1 ) = 2 x 10 5 Pa
Ingcindezi 2 (P 2 ) = 4 x 10 5 Pa
Umqulu 1 (V 1 ) = 1 m 3
Umqulu 2 (V 2 ) = 3 m 3
Okufunwayo: Umsebenzi owenziwe ngegesi kwinqubo i-ABCD (W).
Isixazululo:
Umsebenzi owenziwe yigesi ulingana nendawo ye-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 amaJoules
2. Umsebenzi owenziwa yigesi kwinqubo ye-ABC…
Kwaziwa:
Ingcindezi 1 (P 1 ) = 3 x 10 5 Pa
Ingcindezi 2 (P 2 ) = 6 x 10 5 Pa
Umqulu 1 (V 1 ) = 20 cm 3 = 20 x 10 -6 m 3
Umqulu 2 (V 2 ) = 60 cm 3 = 60 x 10 -6 m 3
Okufunwayo : Umsebenzi owenziwe yigesi kwinqubo ye-ABC
Isixazululo:
Umsebenzi owenziwe ngegesi = indawo ye-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 (amaJoules angu-12)
W = 6 Joule
3. Umdwebo we-PV wegesi esitsheni esivaliwe oboniswe esithombeni esingezansi. Umsebenzi owenziwe yigesi uboniswa ukuthi iyiphi inqubo.
Isixazululo
Inqubo i- AB kanye nenqubo i-DC yizinqubo ze-isobaric (ingcindezi igcinwa ingaguquki) . Inqubo i- AD kanye nenqubo i-BC ziyizinqubo ze - i -choric (ivolumu ayishintshi).
Umsebenzi wenziwa yigesi lapho igesi ikhula (inqubo DC).
Nazi izinkinga nezixazululo ezingu-9 ezihlobene neNqubo ye-Isobaric (Ukucindezela Okuqhubekayo):
Inkinga 1:
Igesi engu-3.0 m³ ngokucindezela okungaguquki icindezelwa ibe ngu-2.0 m³. Uma izinga lokushisa lokuqala lingu-300 K, lingakanani izinga lokushisa lokugcina?
Isixazululo:
Sisebenzisa i-equation yenqubo ye-isobaric: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), singaxazulula izinga lokushisa lokugcina:
\[
\frac{3.0}{300} = \frac{2.0}{T_2} \kusho ukuthi T_2 = \frac{2.0 \izikhathi ezingu-300}{3.0} = 200\, \umbhalo{K}
\]
Inkinga 2:
Bala umsebenzi owenziwe ngama-moles amabili egesi anwebeka ngokungabonakali kusukela ku-1 litre kuya ku-3 litres ku-2 atm.
Isixazululo:
Ukusebenzisa i-equation yomsebenzi owenziwe kwinqubo ye-isobaric: \( W = P \Delta V \):
\[
W = 2\, \text{atm} \times (3 – 1)\, \text{liters} = 4\, \text{atm}\cdot\text{liters}
\]
Inkinga 3:
Iyini ushintsho emandleni angaphakathi lapho ama-mole amane egesi ye-diatomic efanele eshiswa ngokucindezela okungaguquki kusuka ku-200 K kuya ku-300 K?
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwamandla angaphakathi ekucindezelweni okungaguquki kwegesi ye-diatomic: \( \Delta U = nC_pdT \), lapho \( C_p = \frac{7}{2}R \):
\[
\Delta U = 4 \izikhathi \frac{7}{2} \izikhathi 8.314 \izikhathi (300 - 200) \cishe 6990\, \umbhalo{J}
\]
Inkinga 4:
Bala ukushisa okwengezwe ngesikhathi senqubo ye-isobaric lapho ama-moles amabili egesi ye-monatomic ekhula kusuka kumalitha ama-5 kuya kwali-10 ku-400 K.
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa enqubweni ye-isobaric: \( Q = nC_pdT \), lapho \( C_p = \frac{5}{2}R \), kanye \( \frac{V_2}{T_2} = \frac{V_1}{T_1} \):
\[
Q = 2 \izikhathi \frac{5}{2} \izikhathi 8.314 \izikhathi \kwesobunxele(400 \izikhathi \frac{10}{5} – 400\kwesokudla) = 3316\, \umbhalo{J}
\]
Inkinga 5:
Thola ushintsho ku-enthalpy yama-mole amathathu egesi ye-triatomic enwetshwa kusuka ku-1 ilitha kuya ku-2 amalitha ekushiseni okungu-200 K.
Isixazululo:
Ukusebenzisa ifomula yokushintsha kwe-enthalpy yenqubo ye-isobaric: \( \Delta H = nC_pdT \), lapho \( C_p = \frac{f}{2}R \) kanye \( f = 6 \):
\[
\Delta H = 3 \izikhathi \frac{6}{2} \izikhathi 8.314 \izikhathi \kwesobunxele(200 \izikhathi \frac{2}{1} – 200\kwesokudla) = 4989\, \umbhalo{J}
\]
Inkinga 6:
Bala ivolumu yokugcina yama-mole amabili egesi ku-300 K kanye namalitha ama-5 ekuqaleni uma ishiswa ibe ngu-500 K ngokucindezela okungaguquki.
Isixazululo:
Ukusebenzisa i-equation yenqubo ye-isobaric:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2} \kusho V_2 = \frac{V_1 \times T_2}{T_1} = \frac{5 \times 500}{300} \cishe 8.33\, \text{liters}
\]
Inkinga 7:
Thola umsebenzi owenziwe yigesi ye-monatomic uma icindezelwa kusuka kumalitha ayi-6 kuya kwamalitha ama-3 ku-2 atm.
Isixazululo:
Ukusebenzisa i-equation yomsebenzi owenziwe enqubweni ye-isobaric:
\[
W = P \Delta V = 2 \izikhathi (3 - 6) = -6\, \text{atm}\cdot\text{liters}
\]
Inkinga 8:
Igesi ye-diatomic idlula ekukhuleni kwe-isobaric kusuka kumalitha ama-3 kuya kumalitha ama-6 ku-300 K. Thola ushintsho ku-entropy.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwe-entropy enqubweni ye-isobaric yegesi ye-diatomic, lapho \( C_p = \frac{7}{2}R \):
\[
\Delta S = nC_p\ln\frac{T_2}{T_1} + nR\ln\frac{V_2}{V_1} = 2 \izikhathi \frac{7}{2} \izikhathi 8.314 \izikhathi \ln\frac{300 \izikhathi \frac{6}{3}}{300} + 2 \izikhathi 8.314 \izikhathi \ln\frac{6}{3} \cishe 34.76\, \umbhalo{J/K}
\]
Inkinga 9:
Bala ukudluliselwa kokushisa ngesikhathi sokucindezelwa kwe-isobaric kwama-mole ama-5 egesi ye-triatomic kusuka kumalitha ayi-10 kuya kumalitha ama-5 ku-500 K.
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa enqubweni ye-isobaric, lapho \( C_p = \frac{f}{2}R \) kanye \( f = 6 \):
\[
Q = 5 \izikhathi \frac{6}{2} \izikhathi 8.314 \izikhathi \kwesobunxele(500 \izikhathi \frac{5}{10} – 500\kwesokudla) = -12473\, \umbhalo{J}
\]
Lezi zinkinga kufanele zinikeze umbono ophelele wemibono ehlukahlukene ehlobene nenqubo ye-isobaric.
Nazi izinkinga nezixazululo ezingu-9 ezihlobene neNqubo ye-Isothermal (Ukushisa Okuqhubekayo):
Inkinga 1:
Inkinga: Bala umsebenzi owenziwe ama-moles amabili wegesi ekhula kahle ngokusuka ku-1 litre kuya ku-2 litre ku-300 K.
Isixazululo:
Ukusebenzisa i-equation yomsebenzi owenziwe enqubweni ye-isothermal yegesi efanelekile:
\[ W = nRT\ln\frac{V_2}{V_1} \]
\[
W = 2 \izikhathi ezingu-8.314 \izikhathi ezingu-300 \izikhathi \ln\frac{2}{1} \cishe kube ngu-3454\, \umbhalo{J}
\]
Inkinga 2:
Inkinga: Thola ukushisa okudlulisiwe lapho ama-mole amathathu egesi ecindezelwa ngokusuka kumalitha ama-4 kuya kumalitha ama-2 ku-400 K.
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa enqubweni ye-isothermal: \( Q = W \):
\[
Q = 3 \izikhathi ezingu-8.314 \izikhathi ezingu-400 \izikhathi \ln\frac{2}{4} \cishe -3462\, \umbhalo{J}
\]
Inkinga 3:
Thola ushintsho ku-entropy lapho ama-mole angu-4 egesi edlula ekunwetshweni kwe-isothermal kusuka ku-1 litre kuya ku-5 litres ku-300 K.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwe-entropy enqubweni ye-isothermal:
\[
\Delta S = nR\ln\frac{V_2}{V_1} = 4 \izikhathi 8.314 \izikhathi \ln\frac{5}{1} \cishe 46.15\, \umbhalo{J/K}
\]
Inkinga 4:
Bala umsebenzi owenziwe lapho i-mole eyi-1 yegesi efanele icindezelwa ngokusuka kumalitha ayi-6 kuya kumalitha ama-3 ku-200 K.
Isixazululo:
Ukusebenzisa i-equation yomsebenzi owenziwe enqubweni ye-isothermal:
\[
W = 1 \izikhathi 8.314 \izikhathi 200 \izikhathi \ln\frac{3}{6} \cishe -575\, \umbhalo{J}
\]
Inkinga 5:
Nquma ushintsho lwamandla angaphakathi kuma-mole amathathu egesi ngesikhathi sokwanda kwe-isothermal kusuka kumalitha ama-2 kuya kumalitha ayi-6 ekushiseni okulinganayo.
Isixazululo:
Ngenqubo ye-isothermal yegesi efanelekile, ushintsho lwamandla angaphakathi luyi-zero:
\[
\Delta U = 0\, \umbhalo{J}
\]
Inkinga 6:
Bala ukudluliselwa kokushisa lapho ama-mole ama-5 egesi enwetshwa ngokusuka kumalitha ama-3 kuya kumalitha ayi-6 ku-250 K.
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa enqubweni ye-isothermal:
\[
Q = 5 \izikhathi 8.314 \izikhathi 250 \izikhathi \ln\frac{6}{3} \cishe 2879\, \umbhalo{J}
\]
Inkinga 7:
Uyini umsebenzi owenziwa ama-moles amabili egesi ngesikhathi sokucindezela kwe-isothermal kusuka kumalitha ama-4 kuya kumalitha ama-2 ku-150 K?
Isixazululo:
Ukusebenzisa i-equation yomsebenzi owenziwe enqubweni ye-isothermal:
\[
W = 2 \izikhathi 8.314 \izikhathi 150 \izikhathi \ln\frac{2}{4} \cishe -1151\, \umbhalo{J}
\]
Inkinga 8:
Thola ushintsho ku-entropy lapho ama-mole amathathu egesi ecindezelwa ngokusuka kumalitha ama-5 kuya ku-1 ilitha ku-500 K.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwe-entropy enqubweni ye-isothermal:
\[
\Delta S = 3 \izikhathi 8.314 \izikhathi \ln\frac{1}{5} \cishe -34.77\, \umbhalo{J/K}
\]
Inkinga 9:
Thola umsebenzi owenziwe ama-mole angu-4 egesi ekhula kahle ngokusuka kumalitha ama-2 kuya kumalitha ayi-8 ku-100 K.
Isixazululo:
Ukusebenzisa i-equation yomsebenzi owenziwe enqubweni ye-isothermal:
\[
W = 4 \izikhathi ezingu-8.314 \izikhathi ezingu-100 \izikhathi \ln\frac{8}{2} \cishe kube ngu-2304\, \umbhalo{J}
\]
Lezi zinkinga zihlanganisa imiqondo ehlukahlukene ehlobene nenqubo ye-isothermal, njengomsebenzi owenziwe, ukudluliselwa kokushisa, kanye noshintsho ku-entropy.
Nazi izinkinga nezixazululo ezingu-9 ezihlobene neNqubo ye-Isochoric (Umthamo Oqhubekayo):
Inkinga 1:
Bala ushintsho lwamandla angaphakathi ngama-moles amathathu egesi elifanele le-monatomic lapho izinga lokushisa likhuphuka lisuka ku-200 K liye ku-400 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwamandla angaphakathi kuvolumu engaguquki: \( \Delta U = nC_v\Delta T \), lapho \( C_v = \frac{3}{2}R \):
\[
\Delta U = 3 \izikhathi \frac{3}{2} \izikhathi 8.314 \izikhathi (400 - 200) \cishe 3741\, \umbhalo{J}
\]
Inkinga 2:
Thola ukudluliselwa kokushisa kwama-mole amabili egesi ye-diatomic lapho izinga lokushisa lehliswa kusuka ku-300 K kuya ku-200 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa ngevolumu engaguquki: \( Q = \Delta U = nC_v\Delta T \), lapho \( C_v = \frac{5}{2}R \):
\[
Q = 2 \izikhathi \frac{5}{2} \izikhathi 8.314 \izikhathi (200 - 300) \cishe -4157\, \umbhalo{J}
\]
Inkinga 3:
Bala ushintsho ku-entropy ngama-mole angu-4 egesi ye-triatomic lapho izinga lokushisa likhuphuka kusuka ku-100 K kuya ku-300 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwe-entropy kuvolumu engaguquki, lapho \( C_v = \frac{f}{2}R \) kanye \( f = 6 \):
\[
\Delta S = nC_v\ln\frac{T_2}{T_1} = 4 \izikhathi \frac{6}{2} \izikhathi 8.314 \izikhathi \ln\frac{300}{100} \cishe kube ngu-115.36\, \umbhalo{J/K}
\]
Inkinga 4:
Uyini umsebenzi owenziwa yigesi ngesikhathi senqubo ye-isochoric?
Isixazululo:
Njengoba ivolumu ihlala njalo ngesikhathi senqubo ye-isochoric, akukho msebenzi owenziwayo:
\[
W = 0\, \umbhalo{J}
\]
Inkinga 5:
Thola ukudluliselwa kokushisa kwama-mole ama-5 egesi elifanele le-monatomic uma selipholile kusuka ku-500 K kuya ku-300 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa ngevolumu engaguquki, lapho \( C_v = \frac{3}{2}R \):
\[
Q = 5 \izikhathi \frac{3}{2} \izikhathi 8.314 \izikhathi (300 - 500) \cishe -6232\, \umbhalo{J}
\]
Inkinga 6:
Bala ushintsho lwamandla angaphakathi nge-mole eyi-1 yegesi ye-diatomic lapho izinga lokushisa likhuphuka lisuka ku-150 K liye ku-250 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwamandla angaphakathi kuvolumu engaguquki, lapho \( C_v = \frac{5}{2}R \):
\[
\Delta U = 1 \izikhathi \frac{5}{2} \izikhathi 8.314 \izikhathi (250 - 150) \cishe 2079\, \umbhalo{J}
\]
Inkinga 7:
Thola ushintsho ku-entropy yama-mole amathathu egesi ye-monatomic lapho izinga lokushisa lehla kusuka ku-600 K kuya ku-300 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwe-entropy kuvolumu engaguquki, lapho \( C_v = \frac{3}{2}R \):
\[
\Delta S = 3 \izikhathi \frac{3}{2} \izikhathi 8.314 \izikhathi \ln\frac{300}{600} \cishe -34.59\, \umbhalo{J/K}
\]
Inkinga 8:
Kuyini ukudluliselwa kokushisa kwama-moles amabili egesi ye-triatomic uma izinga lokushisa lenyuswa lisuka ku-200 K liye ku-400 K ngevolumu engaguquki?
Isixazululo:
Ukusebenzisa i-equation yokudlulisa ukushisa ngevolumu engaguquki, lapho \( C_v = \frac{6}{2}R \):
\[
Q = 2 \izikhathi \frac{6}{2} \izikhathi 8.314 \izikhathi (400 - 200) \cishe 4986\, \umbhalo{J}
\]
Inkinga 9:
Bala ushintsho lwamandla angaphakathi ngama-moles angu-4 egesi elifanele le-monatomic uma lishiswa kusukela ku-250 K kuya ku-350 K ngevolumu engaguquki.
Isixazululo:
Ukusebenzisa i-equation yokushintsha kwamandla angaphakathi kuvolumu engaguquki, lapho \( C_v = \frac{3}{2}R \):
\[
\Delta U = 4 \izikhathi \frac{3}{2} \izikhathi 8.314 \izikhathi (350 - 250) \cishe 4986\, \umbhalo{J}
\]
Lezi zinkinga zihlanganisa izici ezahlukahlukene zenqubo ye-isochoric, njengokudluliselwa kokushisa, izinguquko emandleni angaphakathi, kanye ne-entropy, yezinhlobo ezahlukene zamagesi.
