30 Kushandiswa kwemutemo wekutanga wethermodynamics mune mamwe maitiro ethermodynamic (Isobaric Isothermal Isochoric)
1. Girafu iri pazasi rinoratidza thermodynamics kutenderera kunoitika negasi. basa zvakaitwa na gasi riri mukuita kwe ABCD riri…
Zvinozivikanwa:
Pressure 1 (P)1) = 2 x 105 Pa
Kumanikidzwa 2 (P)2) = 4 x 105 Pa
Vhoriyamu 1 (V)1) = 1 m3
Vhoriyamu 2 (V)2) = 3 m3
Zvinodiwa: Basa rinoitwa negasi pabasa reABCD (W).
Solution:
Basa rinoitwa negasi rakaenzana nenzvimbo yeABCD.
W = (P)2 - P1)(V)2 - V1)
W = (4 x 10)5 - 2 x 105)(3 – 1)
W = (2 x 10)5)(2)
W = 4 x 105 Joule
2. Basa rinoitwa negasi paABC ndere…
Zvinozivikanwa:
Kumanikidzwa 1 (P)1) = 3 x 105 Pa
Kumanikidzwa 2 (P)2) = 6 x 105 Pa
Vhoriyamu 1 (V)1) = 20 cm3 = 20 x gumi-6 m3
Vhoriyamu 2 (V)2) = 60 cm3 = 60 x gumi-6 m3
Wanted : Basa rakaitwa negasi paABC
Solution:
Basa rinoitwa negasi = nzvimbo yeABC.
W = ½ (P)2 - P1)(V)2 - V1)
W = 1/2 (6 x 10)5 - 3 x 105)(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 (12 Joules)
W = 6 Joule
3. Dhayagiramu yePV yegesi iri mumudziyo wakavharwa inoratidzwa mumufananidzo uri pazasi. Basa rinoitwa negasi rinoratidzwa kuti rinoitwa sei.
mhinduro
Pmaitiro AB uye maitiro DC ndivo maitiro e-isobaric (kumanikidzwa kunoramba kuripo). PMaitiro eAD uye Maitiro eBC ndivo isocmaitiro anotyisa (vhoriyamu haichinji).
Basa racho rakaitwa negasi kana gasi rava kukura (process DC).
Heano matambudziko mapfumbamwe nemhinduro dzine chekuita neIsobaric Process (Constant Pressure):
Dambudziko 1:
Gasi re3.0 m³ parinomanikidzwa nguva dzose rinomanikidzwa kusvika 2.0 m³. Kana tembiricha yekutanga iri 300 K, tembiricha yekupedzisira ndeyei?
Solution:
Tichishandisa equation yemaitiro e isobaric: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), tinogona kugadzirisa tembiricha yekupedzisira:
\[
\frac{3.0}{300} = \frac{2.0}{T_2} \zvinoreva T_2 = \frac{2.0 \kawa 300}{3.0} = 200\, \text{K}
\]
Dambudziko 2:
Verenga basa rakaitwa nemamoles maviri egasi achikura kubva pa1 litre kusvika pa3 litres pa2 atm.
Solution:
Kushandisa equation yebasa rinoitwa mumaitiro e isobaric: \( W = P \Delta V \):
\[
W = 2\, \text{atm} \times (3 – 1)\, \text{liters} = 4\, \text{atm}\cdot\text{liters}
\]
Dambudziko 3:
Chii chinochinja simba remukati kana mamore mana egasi re diatomic rakakodzera achipiswa nekumanikidzwa kwakasimba kubva pa200 K kusvika 300 K?
Solution:
Kushandisa equation yekuchinja kwesimba remukati padanho risingaperi regasi re diatomic: \( \Delta U = nC_pdT \), apo \( C_p = \frac{7}{2}R \):
\[
\Delta U = 4 \nguva \frac{7}{2} \nguva 8.314 \nguva (300 - 200) \inenge 6990\, \text{J}
\]
Dambudziko 4:
Verengai kupisa kwakawedzerwa panguva ye isobaric process apo ma moles maviri egasi re monatomic anokura kubva pa 5 litres kusvika 10 litres pa 400 K.
Solution:
Kushandisa equation yekufambisa kupisa mumaitiro e isobaric: \( Q = nC_pdT \), apo \( C_p = \frac{5}{2}R \), uye \( \frac{V_2}{T_2} = \frac{V_1}{T_1} \):
\[
Q = 2 \nguva \frac{5}{2} \nguva 8.314 \nguva \kuruboshwe(400 \nguva \frac{10}{5} – 400\kurudyi) = 3316\, \text{J}
\]
Dambudziko 5:
Tsvaga shanduko mu enthalpy yemamoles matatu egasi re triatomic rinowedzerwa kubva pa 1 litre kusvika pa 2 litres patembiricha ye 200 K.
Solution:
Kushandisa fomura yekuchinja kwe enthalpy yemaitiro e isobaric: \( \Delta H = nC_pdT \), apo \( C_p = \frac{f}{2}R \) uye \( f = 6 \):
\[
\Delta H = 3 \nguva \frac{6}{2} \nguva 8.314 \nguva \kuruboshwe(200 \nguva \frac{2}{1} – 200\kurudyi) = 4989\, \text{J}
\]
Dambudziko 6:
Verenga huwandu hwekupedzisira hwemamore maviri egasi pa300 K uye marita mashanu pakutanga kana rapiswa kusvika 500 K nekumanikidzwa kwaro nguva dzose.
Solution:
Kushandisa equation yemaitiro e isobaric:
\[
\frac{V_1}{T_1} = \frac{V_2}{T_2} \zvinoreva V_2 = \frac{V_1 \times T_2}{T_1} = \frac{5 \times 500}{300} \approx 8.33\, \text{liters}
\]
Dambudziko 7:
Tsvaga basa rinoitwa negasi remonatomic kana rakamanikidzwa kubva pamarita matanhatu kusvika pamarita matatu pa2 atm.
Solution:
Kushandisa equation yebasa rinoitwa muitiro we isobaric:
\[
W = P \Delta V = 2 \nguva (3 - 6) = -6\, \text{atm}\cdot\text{liters}
\]
Dambudziko 8:
Gasi re diatomu rinowedzerwa ne isobaric kubva pamarita matatu kusvika pamarita matanhatu pa300 K. Tsvaga shanduko mu entropy.
Solution:
Kushandisa equation yekuchinja kwe entropy mumaitiro e isobaric egasi re diatomic, apo \( C_p = \frac{7}{2}R \):
\[
\Delta S = nC_p\ln\frac{T_2}{T_1} + nR\ln\frac{V_2}{V_1} = 2 \nguva \frac{7}{2} \nguva 8.314 \nguva \ln\frac{300 \nguva \frac{6}{3}}{300} + 2 \nguva 8.314 \nguva \ln\frac{6}{3} \approx 34.76\, \text{J/K}
\]
Dambudziko 9:
Verenga kutamiswa kwekupisa panguva yekudzvanywa kwe isobaric kwema moles mashanu egasi re triatomic kubva pamarita gumi kusvika kumarita mashanu pa500 K.
Solution:
Kushandisa equation yekufambisa kupisa mumaitiro e isobaric, apo \( C_p = \frac{f}{2}R \) uye \( f = 6 \):
\[
Q = 5 \nguva \frac{6}{2} \nguva 8.314 \nguva \kuruboshwe(500 \nguva \frac{5}{10} – 500\kurudyi) = -12473\, \text{J}
\]
Matambudziko aya anofanira kupa ruzivo rwakakwana rwepfungwa dzakasiyana-siyana dzine chekuita nemaitiro e-isobaric.
Heano matambudziko mapfumbamwe nemhinduro dzine chekuita neIsothermal Process (Constant Temperature):
Dambudziko 1:
Dambudziko: Verenga basa rakaitwa nemamoles maviri egasi rakanaka rinokura richidzika kubva pa1 litre kusvika pa2 litres pa300 K.
Solution:
Kushandisa equation yebasa rinoitwa mumaitiro e-isothermal kune gasi rakakodzera:
\[ W = nRT\ln\frac{V_2}{V_1} \]
\[
W = 2 \kawa 8.314 \kawa 300 \kawa \ln\frac{2}{1} \approx 3454\, \text{J}
\]
Dambudziko 2:
Dambudziko: Tsvaga kupisa kunotamiswa kana mamore matatu egasi akamanikidzwa kubva pamarita mana kusvika pamarita maviri pa400 K.
Solution:
Kushandisa equation yekufambisa kupisa mumaitiro e isothermal: \( Q = W \):
\[
Q = 3 \kawa 8.314 \kawa 400 \kawa \ln\frac{2}{4} \approx -3462\, \text{J}
\]
Dambudziko 3:
Tsvaga shanduko mu entropy kana ma mole mana egasi akawedzera kubva pa 1 litre kusvika pa 5 litres pa 300 K.
Solution:
Kushandisa equation yekuchinja kwe entropy mumaitiro e isothermal:
\[
\Delta S = nR\ln\frac{V_2}{V_1} = 4 \kawa 8.314 \kawa \ln\frac{5}{1} \anenge 46.15\, \text{J/K}
\]
Dambudziko 4:
Verenga basa rinoitwa kana mole imwe yegesi yakakodzera yadzvanywa isothermally kubva pamarita matanhatu kusvika pamarita matatu pa200 K.
Solution:
Kushandisa equation yebasa rinoitwa mumaitiro e-isothermal:
\[
W = 1 \kawa 8.314 \kawa 200 \kawa \ln\frac{3}{6} \approx -575\, \text{J}
\]
Dambudziko 5:
Tsvaga shanduko yesimba remukati megasi remamoles matatu panguva yekuwedzera kwemafuta kubva pamarita maviri kusvika kumarita matanhatu pakupisa kwakafanana.
Solution:
Kune nzira ye isothermal yegesi yakakodzera, shanduko yesimba remukati i zero:
\[
\Delta U = 0\, \text{J}
\]
Dambudziko 6:
Verenga kutamiswa kwekupisa kana mamore mashanu egasi akawedzerwa isothermally kubva pamarita matatu kusvika kumarita matanhatu pa250 K.
Solution:
Kushandisa equation yekufambisa kupisa mumaitiro e isothermal:
\[
Q = 5 \kawa 8.314 \kawa 250 \kawa \ln\frac{6}{3} \approx 2879\, \text{J}
\]
Dambudziko 7:
Chii chinoitwa nemamoles maviri egasi panguva yekudzvanywa kwemhepo kubva pamarita mana kusvika pamarita maviri pa150 K?
Solution:
Kushandisa equation yebasa rinoitwa mumaitiro e-isothermal:
\[
W = 2 \kawa 8.314 \kawa 150 \kawa \ln\frac{2}{4} \approx -1151\, \text{J}
\]
Dambudziko 8:
Tsvaga shanduko mu entropy kana ma mole matatu egasi akamanikidzwa isothermally kubva pa 5 litres kusvika 1 litre pa 500 K.
Solution:
Kushandisa equation yekuchinja kwe entropy mumaitiro e isothermal:
\[
\Delta S = 3 \kawa 8.314 \kawa \ln\frac{1}{5} \anenge -34.77\, \text{J/K}
\]
Dambudziko 9:
Sarudza basa rinoitwa nemamoles mana egasi rakanaka rinokura kubva pamarita maviri kusvika kumarita masere pa100 K.
Solution:
Kushandisa equation yebasa rinoitwa mumaitiro e-isothermal:
\[
W = 4 \kawa 8.314 \kawa 100 \kawa \ln\frac{8}{2} \approx 2304\, \text{J}
\]
Matambudziko aya anosanganisira pfungwa dzakasiyana-siyana dzine chekuita nemaitiro e-isothermal, dzakadai sebasa rinoitwa, kutamiswa kwekupisa, uye shanduko mu entropy.
Heano matambudziko mapfumbamwe nemhinduro dzine chekuita neIsochoric Process (Constant Volume):
Dambudziko 1:
Verenga shanduko yesimba remukati memuviri we3 moles yegesi yakanaka yemonatomic kana tembiricha yawedzerwa kubva pa200 K kusvika 400 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekuchinja kwesimba remukati pahuwandu husingachinji: \( \Delta U = nC_v\Delta T \), apo \( C_v = \frac{3}{2}R \):
\[
\Delta U = 3 \nguva \frac{3}{2} \nguva 8.314 \nguva (400 - 200) \inenge 3741\, \text{J}
\]
Dambudziko 2:
Sarudza kutamiswa kwekupisa kwema moles maviri egasi re diatomic kana tembiricha yadzikira kubva pa300 K kusvika 200 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekufambisa kupisa pahuwandu husingachinji: \( Q = \Delta U = nC_v\Delta T \), apo \( C_v = \frac{5}{2}R \):
\[
Q = 2 \nguva \frac{5}{2} \nguva 8.314 \nguva (200 - 300) \inenge -4157\, \text{J}
\]
Dambudziko 3:
Verenga shanduko mu entropy yemamoles mana egasi re triatomic kana tembiricha ikawedzera kubva pa100 K kusvika 300 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekuchinja kwe entropy pahuwandu husingachinji, apo \( C_v = \frac{f}{2}R \) uye \( f = 6 \):
\[
\Delta S = nC_v\ln\frac{T_2}{T_1} = 4 \times \frac{6}{2} \times 8.314 \times \ln\frac{300}{100} \approx 115.36\, \text{J/K}
\]
Dambudziko 4:
Chii chinoitwa negasi panguva yekushanda kwe isochoric?
Solution:
Sezvo vhoriyamu ichigara iripo panguva yekushanda kwe isochoric, hapana basa rinoitwa:
\[
W = 0\, \chinyorwa{J}
\]
Dambudziko 5:
Sarudza kuti kupisa kunofambiswa sei kwemamoles mashanu egasi rakanaka remonatomic kana ratonhodzwa kubva pa500 K kusvika 300 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekufambisa kupisa pahuwandu husingachinji, apo \( C_v = \frac{3}{2}R \):
\[
Q = 5 \nguva \frac{3}{2} \nguva 8.314 \nguva (300 - 500) \inenge -6232\, \text{J}
\]
Dambudziko 6:
Verenga shanduko yesimba remukati memunhu mumwe chete wegasi re diatomic kana tembiricha yawedzerwa kubva pa150 K kusvika 250 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekuchinja kwesimba remukati pahuwandu husingachinji, apo \( C_v = \frac{5}{2}R \):
\[
\Delta U = 1 \nguva \frac{5}{2} \nguva 8.314 \nguva (250 - 150) \inenge 2079\, \text{J}
\]
Dambudziko 7:
Tsvaga shanduko mu entropy yema mole matatu egasi re monatomic kana tembiricha yadzikira kubva pa 600 K kusvika 300 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekuchinja kwe entropy pahuwandu husingachinji, apo \( C_v = \frac{3}{2}R \):
\[
\Delta S = 3 \nguva \frac{3}{2} \nguva 8.314 \nguva \ln\frac{300}{600} \anenge -34.59\, \text{J/K}
\]
Dambudziko 8:
Chii chinonzi kutamiswa kwekupisa kwema moles maviri egasi re triatomic kana tembiricha yakawedzerwa kubva pa 200 K kusvika 400 K pahuwandu husingachinji?
Solution:
Kushandisa equation yekufambisa kupisa pahuwandu husingachinji, apo \( C_v = \frac{6}{2}R \):
\[
Q = 2 \nguva \frac{6}{2} \nguva 8.314 \nguva (400 - 200) \inenge 4986\, \text{J}
\]
Dambudziko 9:
Verenga shanduko yesimba remukati memuviri we4 moles yegesi yakanaka yemonatomic kana ichipiswa kubva pa250 K kusvika 350 K pahuwandu husingachinji.
Solution:
Kushandisa equation yekuchinja kwesimba remukati pahuwandu husingachinji, apo \( C_v = \frac{3}{2}R \):
\[
\Delta U = 4 \nguva \frac{3}{2} \nguva 8.314 \nguva (350 - 250) \inenge 4986\, \text{J}
\]
Matambudziko aya anosanganisira zvinhu zvakasiyana-siyana zvemaitiro e isochoric, zvakaita sekuchinjisa kupisa, shanduko musimba remukati, uye entropy, yemhando dzakasiyana dzemagasi.
