F2 - Lesson - 9 PT
F2 - Lesson - 9 PT
F2 - Lesson - 9 PT
trans
Ēc = kT
2 • Isocórico Qisoc = ncv T
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U = N ⇥ kT = nNa ⇥ kT = n ⇥ RT
2 2 2 acordo com 1st Lei da Termodinâmica
U =Q W
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3
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3 3
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monoat
U = N kT = n RT
2 2 n R T = ncv T
2
3
Calor específico -H&R cap 19
• O calor específico molar para um gás ideal em processo • Para outras moléculas, a energia interna continua a ser
isocórico é dada como anteriormente, mas com a particularidade cv
3
<latexit sha1_base64="GxiOzgttqqb7NwyiDDx8JB20A/I=">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</latexit>
2
• A energia interna só depende da temperatura num gás ideal
• Energia interna também com cv • a variação da energia interna depende apenas da variação
monoa da temperatura, independentemente do processo
U = ncv T
<latexit sha1_base64="c7/9wfq12seW+OA8+drXtPnL8VY=">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</latexit>
• Por conseguinte, o cálculo das variações de energia interna • O trabalho do processo isobárico é
pode sempre ser efectuado como se o processo fosse <latexit sha1_base64="UsH1HYolX/7IYH3BhXVzlNHYZN4=">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</latexit>
Z Vf
W isob = P dV = P V = P (Vf Vi ) = P Vf P Vi = nRTf nRTi = nR T
• Para processos isobáricos o trabalho e de acordo com a 1ª • Os calores específicos para processos isobáricos e
lei da Termodinâmica isocóricos estão relacionados por
U =Q W
<latexit sha1_base64="YmoE0aKbPO34ZYXzxUu6fpJ+vuQ=">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</latexit>
cp = cv + R
<latexit sha1_base64="JQ3TkQRH24nW2HHQrCkQjDXhtTk=">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</latexit>
ncv T = Qisob W
<latexit sha1_base64="jmnUFbsgJBlJG6dBFXTgpWkppCQ=">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</latexit>
Trabalho isobárico
ncv T = Qisob P V
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n(cv + R) T = Qisob
para a maior
5
Graus de liberdade-H&R cap 19 Energia de translação de COM
+ rotação de 2 eixos
Energia de translação de COM
+ rotação de 3 eixos
Energia de translação
2
• Cada grau de liberdade contribui com uma energia U
rotação = n RT
2
• As últimas 2 afirmações são o Teorema da Equipartição da • A análise anterior da energia interna e do calor específico pode
6
teoria cinética dos gases - V processos adiabáticos
Expansão adiabática -H&R cap 19 • Uma vez que é um processo adiabático e consideramos um
gás ideal, a lei 1st para o processo de mudança minúscula é
dW ncv dT =
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P dV
Q=0
<latexit sha1_base64="2oNqEhX49gdeEvEF4J/A2SwbO0A=">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</latexit>
nRT
<latexit sha1_base64="rT47Q8Y1Miklz/mbBcIn9n090IE=">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</latexit>
dT R dV
<latexit sha1_base64="F1b2/qYkA1p736+z4xgHfF0MWu0=">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</latexit>
ncv dT = dV
• Sistema bem isolado V =
T cv V
• Processo (suficientemente) mais rápido do que
• Agora, somar todas as pequenas alterações (diferenciais) é
qualquer transferência de calor
equivalente a integrar
• Processo adiabático na expansão/compressão de gás
• Se forem retirados os gritos
Z Z
pequenos, a alteração do volume é dT R dV
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R
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Isolamento
= Ln T = Ln V + c0
muito pequena T cv V cv
R
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cp cv
R
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Ln (T V ) = c0 TV cv = c1 TV cv = constant
também é muito pequeno, pelo que
cv
TV = constant
PV = constant
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(1 )
P T = constant
cp cv
PV cp
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R
PV V = c1 PV = c1 • Também para os gases ideais os calores específicos estão
cv
V cv = c0 cv
nR
ligados à estrutura molecular com os graus de liberdade
f +2
<latexit sha1_base64="+a1iQqruNGxqtvkKfei0mUJ3xHs=">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</latexit>
c2 <latexit sha1_base64="G0D3nCP0+B3D/bH31fwPSMzhvZo=">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</latexit>
PV
<latexit sha1_base64="mAjNP9oNcUiCeOFZfaklYnquNME=">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</latexit>
= constant P =
V
• Também para T e P c1
<latexit sha1_base64="KydplPUDdwOMvRtuAdkb0c5mwLQ=">AAAVY3icjVhfb+PGEVfSNk2UtrnkfE9FgUEP6kkQpIiUc70CIRDXzaW42IKsyFKAk0XQJGUTJimGpFS7xOpD9q1vfen36Mxyl1yKclwBtnbn3/52dnZmVteR7yXpYPDvDz78xS9/9dGvP/6k+elvfvu7z559/sUsWW9i27201/46/vHaSlzfC93L1Et998codq3g2nfn13enxJ9v3Tjx1uE0fYjcq8C6Cb2VZ1spkszPnz+0tN0iuF7fZ7blMwOO+9qb128E6R1rti6MU1j8zfVTC6ZgwCm0p+aqNzW9DjRbkmHqra+hnDRbtrFYxZadnbIs3DNiQAA2FNNWzeiFuUjd+zTzkrWNiEKwzW0pX+FfC36k8sXoEg1fQA/mzVZIFhyCj/OxM9uj5FBDmMCUZTNG/IUXpoKOYiybMkBZTpXyKM4yNMPE3JmRMqpycGchMKjYV+QLiRl0Ef2g2ZrCbJkJOdxOj+Dl0szIxe11mKRWmDIpfGMFgQU97YBAzhNHsOrqLNNZcyzmtqkhULnainjQ1RiqjasgCgCoIZnc8IEVx7Dw3VXalr6coM/GbBF7N7dpp9Tjex0vs7bWy0kd9Ov0Z+xWdqKAqp6yGjBQYdWCZ49Q1b5mIl6eFBoLHsm2SbgLk87jCq0eUHiVMC6NUPX/ZEpxb6BznLkxBopA3KsBwnKzNUcflfZYHopmNjM9tsT/K4ZRbUhQM1x/DG0kI9IZXSqa51McEAk9M5lyAn3jFL/VK8SxaRzbHfdaThkSZaLus+ZgmhoVcQM0vf/VLsf/7st2sPbh+w4e4aXcVLAO1xYr7jr3Tzkmz5wF6KC5Ac7c1NAj+KXnX0P86vf7zRauuXXt7C1G98J21mk+dRKcA8oIpr7HpNgHkNzhHnfIpPVcQGX/wAS1GHAFQsnP5lQYxeteKuHl34GTilSCMoFMHpLPMietq+T2U6boFVwV8hYlhMWAfC+k8ZM57e1S7/DrIXAZhxc3DoJKijSX/LzUFo9CsramvuTJB+OspGk5zfjW/L6td5BFA60jPSf9Rh5UT4PJBPwY30BDkbQYcYtvTdfo3Zku3DdbRHM7Ri+HwYk8Lz65bLfCzkan7MDCe1t5UmXOqTVNjLccu9iE3iHgXKQrt4dHvC9dHKqZ5ZXbdy2HSoeknrGaCPYJSbKJ3d2Nlaii36mi3+3ZwPSk8Gp+aI9POjsnQYTjXfvESTrGeEfJTLjYmYOxn7ggl1By9gD3RyoDKvUCrOX7EMVrGyG7iJZ8gDwvLzBWHK//AWiqi7SVSvNoLwgxu2Dmvagii8iKU8/y4YJlUEwwosdyMaw/5Lze4s6KIgsWgZXexkF2UlwB6hMcDB+ZKAuCWAJbIGxmMH2esfbXg46KoW6UF873NcV8G1fN1kQYPWPZHVVaM0+awGECy3ErFCzlGBd7RJ0JVWWDh2wVt0OHk7yic0ivRCVHYJgySymtkHpFuBUpjTLNo/ZV21U1+BLQbBeX4SOdjloqsWwiDGbuTxuPMXbITBNaNTnjgGUwJryWTKhfhaLi1VRhkWwCM5R59c4MCWiIwARDUaVe90/ysDN5xjY/pKK3wSQtObcnxRYKaSzvPWW6YrKNKsOoYFr84lqxGyWev0YoiXcTVCJWseSGW9zQ8rg8lyx00yctyM7ugKVehRh4KRGhgPt/LCOaxmI1qZFsQgxjUO1zEpnn7i6PyYqRjBXl2MH/vQO2uETFVAVXFbO2ky0JvoZe9wc6dute4CagDZaZPmSCzdOG7btUFhfUfIxMC2o8bJwEjZqejkwPI5ahOHLxPyayA6sAlCiWGfb4uITQBSzs5zg/B0HRdOyJVdg5pPHMGFHrNq9lXGwVsaeam2VHad+u0UWUcFXqNfnNGFMf2aMusspNb+lI90wr3T+9owwcqemNHh4ysalqJCe9dxayylOC+Fy0OKIaisJ7b/pDTY6H2kAOHzOt/QUdp0vDBujD1wPYvVMrpbizPj7F8b2slsl7tUyO5CTCyepenXn3lPUqvLfmyHhb1qO88kUmtiNinMpI0bFt2hJDhzPMWjQUHE6nsD/jLR2eVZYTDNlmZfca3osuDXQ5GNIAG1o+GfFrQ9CjwugIFFNofDksFwx5kD8qgPzzPS49h7fSi3HA24zkpzjNcqklr0rRAX2uPeSvaTk3FMtdMX5Qxv8kGRiqAB5bPH+bUJCeE4BvzczeecDkaySNrZBLl48g8ra31AUcUsBi9oS8uvJSr3ArCJqtQDDPZV54ehX+srrLH0ojGecVliHO6xCPv9vqDPoBZP9VRombVtg3XVNbRB5gBoatfAumsjtC7RoPxG8lvhVcO1bpnPyE0KZUGWHYk+S4ve0Yx0TOr3DhMZ2L0k83xa8NQ9RBExg14GL2POcjJHGpAtUrin2RwfBRgo7eUrtBCzlbGXisJSQGdBBeuEofcsMkBqUcRlvLyEA5WOCxtTWjlgg7wdQl03z2ctAf8A/UB5oYvGyIz9h89i+s//YmcMPU9q0kea8NovQqE9WGNRebxI0s+866cd/jMLTweK8y/hshgxZSHFitY/zDTpxTVY3MCpLkIaDfKqhIJvs8Ih7ivd+kqzdXmRdGm9QN7Xyh1QYb6jXQD47geLFrp/4DDiw79hAr2LcWeiJ146SJTtD2t1wfzPS+9rp/fHH88pu/Cnd83Ph944+NdkNr/LnxTePvjXHjsmE//8/RR0efHT07+u+LT1988eIoF/3wA6HzvFH5vPjD/wCK3VBr</latexit>
P = f
V 2 +1
✓ ◆
<latexit sha1_base64="EDsIGk4vPmqOJFeSc374txvZhlc=">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</latexit>
nRT
<latexit sha1_base64="Xjyk39669FKoaA4rkQS8QXQLgzw=">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</latexit>
(1 )
P
P
= c0 P T = constant
9
Expansão livre -H&R cap 19
• (Relembrar diapositivo 4) A expansão livre é um processo adiabático especial em que não é efectuado qualquer
trabalho
• Não há alteração da energia interna, do trabalho ou da transferência de calor
• Todos os resultados anteriores daUexpansão
= 0 adiabática não se aplicam à expansão livre, embora esta seja
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Ti = Tf
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adiabática Arredores
sistema
• Assim, para gases ideais
• Note-se que o volume aqui é antes e depois da expansão, e não um volume que se expande para o meio envolvente
tornando possível o trabalho
10