Amfani da dokar farko ta thermodynamics a cikin wasu hanyoyin thermodynamic (Isobaric Isothermal Isochoric)

30 Amfani da dokar farko ta thermodynamics a cikin wasu hanyoyin thermodynamic (Isobaric Isothermal Isochoric)

1. Jadawalin da ke ƙasa yana nuna zagayowar thermodynamic da gas ke fuskanta. Aikin da gas ke yi akan tsarin ABCD shine…

An sani:

Matsi 1 (P1 ₎ = 2 x 10 ⁵ Pa

Matsi na 2 (P2 ₎ = 4 x 10 ⁵ Pa

Juzu'i na 1 (V ₁ ) = 1 m ³

Juzu'i na 2 (V ₂ ) = 3 m ³

Ana so: Aikin da gas ke yi akan tsarin ABCD (W).

Magani:

Aikin da iskar gas ke yi daidai yake da yankin 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 = Joules 4 x ¹⁰⁵

2. Aikin da gas ke yi akan tsarin ABC shine…

An sani:

Matsi na 1 (P1 ₎ = 3 x 10 ⁵ Pa

Matsi na 2 (P2 ₎ = 6 x 10 ⁵ Pa

Juzu'i na 1 (V ₁ ) = 20 cm ³ = 20 x 10 ^-6 m ³

Juzu'i na 2 (V ₂ ) = 60 cm ³ = 60 x 10 ^-6 m ³

Ana so : Aikin da gas ke yi akan tsarin ABC

Magani:

Aikin da ake yi da iskar gas = yankin 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 (Joules 12)

W = Joule 6

3. Zane na PV na iskar gas a cikin akwati mai rufewa da aka nuna a cikin hoton da ke ƙasa. An nuna aikin da iskar gas ɗin ta yi a cikin wane tsari.

Magani

Tsarin AB da tsari DC matakai ne na isobaric (matsin lamba yana tsayawa akai-akai) . Tsarin AD da tsari BC matakai ne na choric ( ƙara ba ya canzawa).

An yi aikin ne ta hanyar iskar gas lokacin da iskar gas ta faɗaɗa (tsarin DC).

Ga matsaloli 9 da mafita da suka shafi Tsarin Isobaric (Matsi Mai Dorewa):

Matsala ta 1:
Ana matse iskar gas mai girman m³ 3.0 a matsin lamba akai-akai zuwa m³ 2.0. Idan zafin farko shine 300 K, menene zafin ƙarshe?

Magani:
Ta amfani da lissafi don tsarin isobaric: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), za mu iya warware zafin ƙarshe:

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

Matsala ta 2:
Lissafa aikin da moles 2 na iskar gas ke yi yana faɗaɗa isobarically daga lita 1 zuwa lita 3 a 2 atm.

Magani:
Amfani da lissafin aikin da aka yi a cikin tsarin isobaric: \( W = P \Delta V \):

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

Matsala ta 3:
Menene canjin makamashin ciki idan aka dumama moles 4 na iskar diatomic mai kyau a matsin lamba akai-akai daga 200 K zuwa 300 K?

Magani:
Amfani da lissafin canjin kuzarin ciki a matsin lamba akai-akai ga iskar diatomic: \( \Delta U = nC_pdT \), inda \( C_p = \frac{7}{2}R \):

\[
\Delta U = sau 4 \frac{7}{2} \sau 8.314 \sau (300 - 200) \sau 6990\, \text{J}
\]

Matsala ta 4:
Lissafa zafin da aka ƙara yayin aikin isobaric lokacin da moles 2 na iskar gas mai motsi ke faɗaɗa daga lita 5 zuwa lita 10 a 400 K.

Magani:
Amfani da lissafin canja wurin zafi a cikin tsarin isobaric: \( Q = nC_pdT \), inda \( C_p = \frac{5}{2}R \), da \( \frac{V_2}{T_2} = \frac{V_1}{T_1} \):

\[
Q = 2 \sau \frac{5}{2} \sau 8.314 \sau \left(400 \sau \frac{10}{5} – 400\right) = 3316\, \text{J}
\]

Matsala ta 5:
Ƙayyade canjin enthalpy na moles 3 na iskar triatomic wanda aka faɗaɗa daga lita 1 zuwa lita 2 a zafin jiki na 200 K.

Magani:
Amfani da dabarar canjin enthalpy don tsarin isobaric: \( \Delta H = nC_pdT \), inda \( C_p = \frac{f}{2}R \) da \( f = 6 \):

\[
\Delta H = sau 3 \frac{6}{2} \sau 8.314 \sau \left(200 \sau \frac{2}{1} – 200\right) = 4989\, \text{J}
\]

Matsala ta 6:
A ƙididdige ƙarar ƙarshe ta moles 2 na iskar gas a 300 K da lita 5 da farko lokacin da aka dumama shi zuwa 500 K a matsin lamba akai-akai.

Magani:
Amfani da lissafin don tsarin isobaric:

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

Matsala ta 7:
Nemo aikin da iskar gas mai suna monatomic ke yi lokacin da aka matse shi daga lita 6 zuwa lita 3 a 2 atm.

Magani:
Amfani da lissafin aikin da aka yi a cikin tsarin isobaric:

\[
W = P \Delta V = sau 2 (3 - 6) = -6\, \text{atm}\cdot\text{lita}
\]

Matsala ta 8:
Iskar diatomic tana fuskantar faɗaɗa isobaric daga lita 3 zuwa lita 6 a 300 K. Nemo canjin entropy.

Magani:
Amfani da lissafin canjin entropy a cikin tsarin isobaric don iskar diatomic, inda \(C_p = \frac{7}{2}R \):

\[
\Delta S = nC_p\ln\frac{T_2}{T_1} + nR\ln\frac{V_2}{V_1} = 2 \times \frac{7}{2} \times 8.314 \times \ln\frac{300 \times \frac{6}{3}}{300} + 2 \times 8.314 \times \ln\frac{6}{3} \approx 34.76\, \text{J/K}
\]

Matsala ta 9:
Lissafa canja wurin zafi yayin matsewar isobaric na moles 5 na iskar triatomic daga lita 10 zuwa lita 5 a 500 K.

Magani:
Amfani da lissafin canja wurin zafi a cikin tsarin isobaric, inda \(C_p = \frac{f}{2}R \) da \(f = 6 \):

\[
Q = 5 \sau \frac{6}{2} \sau 8.314 \sau \left(500 \sau \frac{5}{10} – 500\right) = -12473\, \text{J}
\]

Waɗannan matsalolin ya kamata su ba da cikakken bayani game da ra'ayoyi daban-daban da suka shafi tsarin isobaric.

Ga matsaloli 9 da mafita da suka shafi Tsarin Isothermal (Zafin jiki Mai Tsayi):

 Matsala ta 1:
Matsala: Lissafa aikin da moles 2 na iskar gas mai kyau ke yi yana faɗaɗawa a cikin yanayi mai zafi daga lita 1 zuwa lita 2 a 300 K.

Magani:
Amfani da lissafin aikin da aka yi a cikin tsarin isothermal don iskar gas mai kyau:
\[ W = nRT\ln\frac{V_2}{V_1} \]

\[
W = 2 \sau 8.314 \sau 300 \sau \ln\frac{2}{1} \approx 3454\, \text{J}
\]

Matsala ta 2:
Matsala: Nemo zafin da aka canja lokacin da aka matse moles 3 na iskar gas a cikin yanayi mai zafi daga lita 4 zuwa lita 2 a 400 K.

Magani:
Amfani da lissafin canja wurin zafi a cikin tsarin isothermal: \( Q = W \):

\[
Q = sau 3 8.314 \sau 400 \sau \ln\frac{2}{4} \approx -3462\, \text{J}
\]

Matsala ta 3:
Ƙayyade canjin entropy lokacin da moles 4 na iskar gas suka sami faɗaɗawar isothermal daga lita 1 zuwa lita 5 a 300 K.

Magani:
Amfani da lissafi don canjin entropy a cikin tsarin isothermal:

\[
\Delta S = nR\ln\frac{V_2}{V_1} = 4 \sau 8.314 \sau \ln\frac{5}{1} \approx 46.15\, \text{J/K}
\]

Matsala ta 4:
Lissafa aikin da aka yi lokacin da aka matse mole 1 na iskar gas mai kyau a cikin yanayi mai zafi daga lita 6 zuwa lita 3 a 200 K.

Magani:
Amfani da lissafin aikin da aka yi a cikin tsarin isothermal:

\[
W = 1 \sau 8.314 \sau 200 \sau \ln\frac{3}{6} \approx -575\, \text{J}
\]

Matsala ta 5:
Kayyade canjin makamashin ciki na moles 3 na iskar gas yayin faɗaɗawar isothermal daga lita 2 zuwa lita 6 a yanayin zafi mai ɗorewa.

Magani:
Don tsarin isothermal na iskar gas mai kyau, canjin makamashin ciki sifili ne:

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

Matsala ta 6:
Lissafa canja wurin zafi lokacin da aka faɗaɗa moles 5 na iskar gas a cikin yanayi mai zafi daga lita 3 zuwa lita 6 a 250 K.

Magani:
Amfani da lissafin canja wurin zafi a cikin tsarin isothermal:

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

Matsala ta 7:
Menene aikin da moles 2 na iskar gas ke yi yayin matsewar isothermal daga lita 4 zuwa lita 2 a 150 K?

Magani:
Amfani da lissafin aikin da aka yi a cikin tsarin isothermal:

\[
W = 2 \sau 8.314 \sau 150 \sau \ln\frac{2}{4} \approx -1151\, \text{J}
\]

Matsala ta 8:
Nemo canjin entropy lokacin da aka matse moles 3 na iskar gas a cikin yanayi mai zafi daga lita 5 zuwa lita 1 a 500 K.

Magani:
Amfani da lissafi don canjin entropy a cikin tsarin isothermal:

\[
\Delta S = sau 3 \sau 8.314 \sau \ln\frac{1}{5} \approx -34.77\, \text{J/K}
\]

Matsala ta 9:
Ƙayyade aikin da aka yi ta hanyar moles 4 na iskar gas mai kyau wanda ke faɗaɗa a cikin yanayi mai zafi daga lita 2 zuwa lita 8 a 100 K.

Magani:
Amfani da lissafin aikin da aka yi a cikin tsarin isothermal:

\[
W = 4 \sau 8.314 \sau 100 \sau \ln\frac{8}{2} \approx 2304\, \text{J}
\]

Waɗannan matsalolin sun shafi ra'ayoyi daban-daban da suka shafi tsarin isothermal, kamar aikin da aka yi, canja wurin zafi, da canjin entropy.

Ga matsaloli 9 da mafita da suka shafi Tsarin Isochoric (Constant Volume):

Matsala ta 1:
Lissafa canjin makamashin ciki na moles 3 na iskar gas mai kyau ta monatomic lokacin da aka ƙara zafin jiki daga 200 K zuwa 400 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafin don canji a cikin kuzarin ciki a cikin ƙarar da ba ta canzawa: \( \Delta U = nC_v\Delta T \), inda \( C_v = \frac{3}{2}R \):

\[
\Delta U = sau 3 \frac{3}{2} \sau 8.314 \sau (400 - 200) \sau 3741\, \text{J}
\]

Matsala ta 2:
Ƙayyade canja wurin zafi don moles 2 na iskar diatomic lokacin da zafin jiki ya ragu daga 300 K zuwa 200 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafi don canja wurin zafi a ƙarar da ba ta canzawa: \( Q = \Delta U = nC_v\Delta T \), inda \( C_v = \frac{5}{2}R \):

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

Matsala ta 3:
Lissafa canjin entropy ga moles 4 na iskar triatomic lokacin da zafin jiki ya ƙaru daga 100 K zuwa 300 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafi don canjin entropy a madaidaicin girma, inda \(C_v = \frac{f}{2}R \) da \(f = 6 \):

\[
\Delta S = nC_v\ln\frac{T_2}{T_1} = 4 \sau \frac{6}{2} \sau 8.314 \sau \ln\frac{300}{100} \approx 115.36\, \text{J/K}
\]

Matsala ta 4:
Menene aikin da iskar gas ke yi yayin aikin isochoric?

Magani:
Tunda ƙarar ta kasance mai ɗorewa yayin tsarin isochoric, babu wani aiki da aka yi:

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

Matsala ta 5:
Kayyade canja wurin zafi na moles 5 na iskar gas mai kyau ta monatomic lokacin da aka sanyaya ta daga 500 K zuwa 300 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafi don canja wurin zafi a ƙarar da ba ta canzawa, inda \(C_v = \frac{3}{2}R \):

\[
Q = 5 \sau \frac{3}{2} \sau 8.314 \sau (300 - 500) \sau -6232\, \text{J}
\]

Matsala ta 6:
Lissafa canjin makamashin ciki don mole 1 na iskar diatomic lokacin da aka ƙara zafin jiki daga 150 K zuwa 250 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafin don canji a cikin kuzarin ciki a madaidaicin ƙara, inda \(C_v = \frac{5}{2}R \):

\[
\Delta U = sau 1 \frac{5}{2} \sau 8.314 \sau (250 - 150) \sau 2079\, \text{J}
\]

Matsala ta 7:
Ƙayyade canjin entropy ga moles 3 na iskar gas mai motsi lokacin da zafin jiki ya ragu daga 600 K zuwa 300 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafi don canjin entropy a madaidaicin girma, inda \(C_v = \frac{3}{2}R \):

\[
\Delta S = sau 3 \frac{3}{2} \sau 8.314 \sau \ln\frac{300}{600} \approx -34.59\, \text{J/K}
\]

Matsala ta 8:
Menene canja wurin zafi ga moles 2 na iskar gas ta triatomic lokacin da aka ƙara zafin jiki daga 200 K zuwa 400 K a yawan da ba ya canzawa?

Magani:
Amfani da lissafi don canja wurin zafi a ƙarar da ba ta canzawa, inda \(C_v = \frac{6}{2}R \):

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

Matsala ta 9:
Lissafa canjin makamashin ciki na moles 4 na iskar gas mai kyau ta monatomic lokacin da aka dumama ta daga 250 K zuwa 350 K a yawan da ba ya canzawa.

Magani:
Amfani da lissafin don canji a cikin kuzarin ciki a madaidaicin ƙara, inda \(C_v = \frac{3}{2}R \):

\[
\Delta U = sau 4 \frac{3}{2} \sau 8.314 \sau (350 - 250) \sau 4986\, \text{J}
\]

Waɗannan matsalolin sun shafi fannoni daban-daban na tsarin isochoric, kamar canja wurin zafi, canje-canje a cikin makamashin ciki, da entropy, na nau'ikan iskar gas daban-daban.