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A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ideal gas [Cp = 1000 J/(kg.K) and Cv = 800 J/(kg.K)] at a pressure of 105 Pa. A stirrer is rotated at constant rpm in the container for 1000 rotations and the applied torque is 100 N-m. The final temperature of the gas (in K) is _________.
(Important - Enter only the numerical value in the answer)
Correct answer is '1128.31'. Can you explain this answer?
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A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ...
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Given data:
- Volume of the container (V) = 1 m^3
- Mass of the gas (m) = 1.0 kg
- Specific heat at constant pressure (Cp) = 1000 J/(kg.K)
- Specific heat at constant volume (Cv) = 800 J/(kg.K)
- Pressure of the gas (P) = 105 Pa
- Applied torque (T) = 100 N-m
- Number of rotations of the stirrer (N) = 1000
Assumptions:
- The gas behaves as an ideal gas.
- The process is adiabatic (no heat exchange with the surroundings).
- The process is reversible.
- The gas is in thermal equilibrium throughout the process.
Process:
1. Calculate the work done by the stirrer using the formula:
Work (W) = Torque (T) × Number of rotations (N)
2. Use the ideal gas equation to find the initial temperature (T1) of the gas:
PV = mRT1
R = Cp - Cv (gas constant for an ideal gas)
T1 = PV / (mR)
3. Determine the change in internal energy (ΔU) using the first law of thermodynamics:
ΔU = Q - W
Q = 0 (adiabatic process, no heat exchange)
ΔU = -W
4. Calculate the change in temperature (ΔT) using the equation:
ΔU = mCvΔT
ΔT = ΔU / (mCv)
5. Determine the final temperature (T2) of the gas:
T2 = T1 + ΔT
Calculation:
1. Work done by the stirrer:
W = T × N = 100 N-m × 1000 rotations = 100,000 N-m
2. Ideal gas equation:
R = Cp - Cv = 1000 J/(kg.K) - 800 J/(kg.K) = 200 J/(kg.K)
T1 = PV / (mR) = (105 Pa × 1 m^3) / (1.0 kg × 200 J/(kg.K)) = 0.525 K
3. Change in internal energy:
ΔU = -W = -100,000 N-m
4. Change in temperature:
ΔT = ΔU / (mCv) = (-100,000 N-m) / (1.0 kg × 800 J/(kg.K)) = -125 K
5. Final temperature:
T2 = T1 + ΔT = 0.525 K - 125 K = -124.475 K
Conclusion:
The final temperature of the gas is approximately -124.475 K. However, this result is not physically meaningful because a negative temperature is not possible. It is likely that there was an error in the calculation or some assumption made in the problem statement.
- Volume of the container (V) = 1 m^3
- Mass of the gas (m) = 1.0 kg
- Specific heat at constant pressure (Cp) = 1000 J/(kg.K)
- Specific heat at constant volume (Cv) = 800 J/(kg.K)
- Pressure of the gas (P) = 105 Pa
- Applied torque (T) = 100 N-m
- Number of rotations of the stirrer (N) = 1000
Assumptions:
- The gas behaves as an ideal gas.
- The process is adiabatic (no heat exchange with the surroundings).
- The process is reversible.
- The gas is in thermal equilibrium throughout the process.
Process:
1. Calculate the work done by the stirrer using the formula:
Work (W) = Torque (T) × Number of rotations (N)
2. Use the ideal gas equation to find the initial temperature (T1) of the gas:
PV = mRT1
R = Cp - Cv (gas constant for an ideal gas)
T1 = PV / (mR)
3. Determine the change in internal energy (ΔU) using the first law of thermodynamics:
ΔU = Q - W
Q = 0 (adiabatic process, no heat exchange)
ΔU = -W
4. Calculate the change in temperature (ΔT) using the equation:
ΔU = mCvΔT
ΔT = ΔU / (mCv)
5. Determine the final temperature (T2) of the gas:
T2 = T1 + ΔT
Calculation:
1. Work done by the stirrer:
W = T × N = 100 N-m × 1000 rotations = 100,000 N-m
2. Ideal gas equation:
R = Cp - Cv = 1000 J/(kg.K) - 800 J/(kg.K) = 200 J/(kg.K)
T1 = PV / (mR) = (105 Pa × 1 m^3) / (1.0 kg × 200 J/(kg.K)) = 0.525 K
3. Change in internal energy:
ΔU = -W = -100,000 N-m
4. Change in temperature:
ΔT = ΔU / (mCv) = (-100,000 N-m) / (1.0 kg × 800 J/(kg.K)) = -125 K
5. Final temperature:
T2 = T1 + ΔT = 0.525 K - 125 K = -124.475 K
Conclusion:
The final temperature of the gas is approximately -124.475 K. However, this result is not physically meaningful because a negative temperature is not possible. It is likely that there was an error in the calculation or some assumption made in the problem statement.
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A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ...
No my dear correct ans is 1285.39 K
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A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ideal gas [Cp = 1000J/(kg.K) and Cv = 800 J/(kg.K)] at a pressure of 105 Pa. A stirrer is rotated at constant rpm inthe container for 1000 rotations and the applied torque is 100 N-m. The final temperature ofthe gas (in K) is _________.(Important - Enter only the numerical value in the answer)Correct answer is '1128.31'. Can you explain this answer?
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A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ideal gas [Cp = 1000J/(kg.K) and Cv = 800 J/(kg.K)] at a pressure of 105 Pa. A stirrer is rotated at constant rpm inthe container for 1000 rotations and the applied torque is 100 N-m. The final temperature ofthe gas (in K) is _________.(Important - Enter only the numerical value in the answer)Correct answer is '1128.31'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ideal gas [Cp = 1000J/(kg.K) and Cv = 800 J/(kg.K)] at a pressure of 105 Pa. A stirrer is rotated at constant rpm inthe container for 1000 rotations and the applied torque is 100 N-m. The final temperature ofthe gas (in K) is _________.(Important - Enter only the numerical value in the answer)Correct answer is '1128.31'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A well insulated rigid container of volume 1 m3 contains 1.0 kg of an ideal gas [Cp = 1000J/(kg.K) and Cv = 800 J/(kg.K)] at a pressure of 105 Pa. A stirrer is rotated at constant rpm inthe container for 1000 rotations and the applied torque is 100 N-m. The final temperature ofthe gas (in K) is _________.(Important - Enter only the numerical value in the answer)Correct answer is '1128.31'. Can you explain this answer?.
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