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One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at constant volume, cn = 1000J/kg.K) at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100kJ of work is done on the system by a stirrer. The increase in entropy of the system is _________ J/K.
Correct answer is between '286,288'. Can you explain this answer?
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One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at...
Given that m = 1kg, R = 400 kJ/kgK, CV = 1000 J/kgK
P1 = 1 bar, T1 = 300 K
P1 = 1 bar, T1 = 300 K
Since the gas is contained in a sealed rigid cylinder, and given that adiabatic process is done to the system, means no heat is transferred from/to the system, Q = 0 And we know from first law of thermo dynamics,
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One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at...
Calculation of Increase in Entropy
- Given data: R = 400 J/kg.K, cv = 1000 J/kg.K, work done on the system = 100 kJ = 100,000 J
- Initial state: P1 = 1 bar, T1 = 300 K
- Final state: Adiabatic process, so Q = 0
- First Law of Thermodynamics: ΔU = Q - W, where ΔU = cvΔT
Step 1: Calculate the final temperature
- Since the process is adiabatic, Q = 0
- From the first law of thermodynamics: ΔU = cvΔT = -W
- ΔT = -W/cv = -100,000 J / 1000 J/kg.K = -100 K
- T2 = T1 + ΔT = 300 K - 100 K = 200 K
Step 2: Calculate the change in entropy
- Entropy change for an adiabatic process is: ΔS = cv * ln(T2/T1) - R * ln(P2/P1)
- ln(P2/P1) = ln(1) = 0 (since it's a sealed rigid cylinder)
- ΔS = cv * ln(T2/T1) = 1000 J/kg.K * ln(200/300) = 1000 J/kg.K * ln(2/3)
- ΔS ≈ 1000 J/kg.K * (-0.4055) ≈ -405.5 J/kg.K
Step 3: Convert the entropy change to total system entropy change
- Total mass of the gas = 1 kg
- Total entropy change = m * ΔS = 1 kg * (-405.5 J/kg.K) ≈ -405.5 J/K
Therefore, the increase in entropy of the system is approximately 405.5 J/K.
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One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at constant volume, cn = 1000J/kg.K) at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100kJ of work is done on the system by a stirrer. The increase in entropy of the system is _________ J/K.Correct answer is between '286,288'. Can you explain this answer?
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