O ar está expandindo em um sistema de pistão–cilindro de modo que
em
. O trabalho, quando o volume muda de
para
é mais próximo de:
(A) 20 kJ
(B) 25 kJ
(C) 40 kJ
(D) 55 kJ
(A) 20 kJ
(B) 25 kJ
(C) 40 kJ
(D) 55 kJ
Passo 1
O enunciado dá a relação
com
em
e
em
. O volume muda de
para
. A pergunta é: qual o trabalho realizado durante essa transformação? (escolhas: (A)
, (B)
, (C)
, (D)
).
Passo 2
Recordando a definição física do trabalho em um processo quasistático de pistão:
Aqui
tem unidades de pressão vezes volume. Como
está em
e
em
, a unidade resultante
é igual a
. Isso significa que, ao integrar com
em
e
em
, o resultado já sai em
— bom para a prova, sem conversões extras.
Passo 3
Usando a relação fornecida, isolamos
:
Agora substituímos na integral do trabalho.
Passo 4
Montamos a integral e explico a técnica de integração que vou usar. A integral é
Regra de potência para integrais: para
,
Aqui
, então
Multiplicando pelo fator
, o antiderivado é
.
Passo 5
Avalio a primitiva nos limites:
Calculo passo a passo:
Portanto
Como explicado no Passo 2, o valor
está em
, ou seja em
. Logo o trabalho é
, que corresponde à alternativa (C)."]))])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])])+) ]
está em
, ou seja em
. Logo o trabalho é
, que corresponde à alternativa (C)."}))]))
"]
"))
print(default_api.SolutionSteps(solution_steps=[)
"]
"))
print(default_api.SolutionSteps(solution_steps=[)
Resposta
(C) 40 kJ