Help (4). Suppose we take n moles of a monatomic ideal gas through the following reversible cycle: AB is an isobariccompression; BC is an adiabatic expansion; CD is an isothermal expansion; DA is a constant volume pressureΔQincrease completing the cycle. (a) Show the cycle on a PV-diagram. (b) Express the heat flow, work Wchange in internal energyДЕthe change in entropyFint ,ASfor the legs AB, BC, and CD in terms of number ofmoles n, universal ideal gas constant R, 'ATA To., andTo

Answered: (4). Suppose we take n moles of a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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(4). Suppose we take n moles of a monatomic ideal gas through the following reversible cycle: AB is an isobaric
compression; BC is an adiabatic expansion; CD is an isothermal expansion; DA is a constant volume pressure
ΔQ
increase completing the cycle. (a) Show the cycle on a PV-diagram. (b) Express the heat flow
, work W
change in internal energy
ДЕ
the change in entropy
Fint ,
AS
for the legs AB, BC, and CD in terms of number of
moles n, universal ideal gas constant R, 'A
TA To.
, and
To

Expert Solution

Step 1 P- V diagram

a) P-v diagram of given process:-

b) For isobaric process AB:-

$H e a t f l o w f r o m A T o B a s c o n s \tan t p r e s s u r e δ Q = n c_{p} d T δ Q = n c_{p} (T_{B} - T_{A}) δ Q = n \times \frac{γ R}{γ - 1} (T_{B} - T_{A}) w h e r e γ = a d i a b a t i c i n d e x f o r m o n o a t o m i c w h e r e c_{p} = s p e c i f i c h e a t c a p a c i t y a t c o n s \tan t p r e s s u r e f o r m o n o a t o m i c i d e a l g a s A n d W o r k δ W = P d v W_{1, 2} = P (v_{B} - V_{A}) W_{1, 2} = P V_{A} (\frac{V_{B}}{V_{A}} - 1) S i n c e P V = n R T S o \frac{V_{B}}{V_{A}} = \frac{T_{B}}{T_{A}} a n d P V_{A} = n R T_{A} W_{1, 2} = n R T_{A} (\frac{T_{B}}{T_{A}} - 1) N o w b y t h e r m o d y n a m i c s 1^{r s t} l a w δ Q = d E + δ W d E = δ Q - δ W d E = n \times \frac{γ R}{γ - 1} (T_{B} - T_{A}) - n R T_{A} (\frac{T_{B}}{T_{A}} - 1) O n s i m p l i f i c a t i o n d E = \frac{n R T_{A}}{γ - 1} (\frac{T_{B}}{T_{A}} - 1) A n d f r o m T - d s e q u a t i o n T d s = d h - v d p$

$T d s = n c_{p} d T - v d p d s = \frac{n γ R}{y - 1} \frac{d T}{T} - \frac{v}{T} d p \sin c e P V = n R T s o \frac{V}{T} = \frac{n R}{P} d s = \frac{n γ R}{y - 1} \frac{d T}{T} - \frac{n R}{P} d p o n i n t e g r a t e ∆ s = \frac{n γ R}{y - 1} \times \ln (\frac{T_{B}}{T_{A}}) - n R \ln (\frac{P_{B}}{P_{A}}) \sin c e p r o c e s s i s i s o b a r i c s o P_{A} = P_{B} ∆ s = \frac{n γ R}{y - 1} \times \ln (\frac{T_{B}}{T_{A}})$

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