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One kg of air (R=287 J/kg-K) goes through an irreversible process between two equilibrium states, 1 (30°C, 1.2 m3) and state 2 (30°C, 0.8 m3). What is the change in entropy (in J/kg-K)?
  • a)
    -116.36
  • b)
    -50.53
  • c)
    50.53
  • d)
    116.36
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
One kg of air (R=287 J/kg-K) goes through an irreversible process bet...
Entropy changes for a closed system
For constant volume:
s2−s1 = cv lnT2/T1
For constant pressure:
s2−s1 = cp lnT2/T1
For constant temperature process:
s2−s1 = R ln v2/v1
For adiabatic process (Reversible):
dQ = 0 ⇒ dS = 0
Calculation:
Here T1 = T2
So the process is isothermal.
s2−s1 = R ln v2/v1
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Most Upvoted Answer
One kg of air (R=287 J/kg-K) goes through an irreversible process bet...

The change in entropy can be calculated using the equation:

ΔS = m · Cp · ln(T2/T1) - R · ln(V2/V1)

Given:
m = 1 kg (mass of air)
Cp = specific heat capacity of air at constant pressure = 1005 J/kg-K
R = 287 J/kg-K
T1 = 30°C = 303 K (temperature at state 1)
T2 = 30°C = 303 K (temperature at state 2)
V1 = 1.2 m^3 (volume at state 1)
V2 = 0.8 m^3 (volume at state 2)

Let's calculate each term of the equation:

Term 1: m · Cp · ln(T2/T1)
= 1 kg · 1005 J/kg-K · ln(303/303)
= 1 kg · 1005 J/kg-K · ln(1)
= 1 kg · 1005 J/kg-K · 0
= 0 J/K

Term 2: R · ln(V2/V1)
= 287 J/kg-K · ln(0.8/1.2)
= 287 J/kg-K · ln(0.66)
= 287 J/kg-K · (-0.415)
= -119.405 J/K

Therefore, the change in entropy is:
ΔS = 0 J/K - (-119.405 J/K)
ΔS = -(-119.405) J/K
ΔS = 119.405 J/K

Since the question asks for the change in entropy in J/kg-K, we divide by the mass of air:
Change in entropy = 119.405 J/K / 1 kg
Change in entropy = 119.405 J/kg-K

The closest option to 119.405 J/kg-K is option 'A' (-116.36 J/kg-K).
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One kg of air (R=287 J/kg-K) goes through an irreversible process between two equilibrium states, 1 (30°C, 1.2 m3) and state 2 (30°C, 0.8 m3). What is the change in entropy (in J/kg-K)?a)-116.36b)-50.53c)50.53d)116.36Correct answer is option 'A'. Can you explain this answer?
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