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The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case of
- a)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.
- b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.
- c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.
- d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.
Correct answer is option 'C'. Can you explain this answer?
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The heat transfer, Q, the work done W and the change in internal energ...
In example of (c), it is a case of free expansion heat transfer, work done, and changes in internal energy are all zero.
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The heat transfer, Q, the work done W and the change in internal energ...
Heat transfer, work done, and change in internal energy
Heat transfer (Q), work done (W), and change in internal energy (ΔU) are all related to the energy exchange in a system. In different scenarios, one or more of these quantities may be zero. Let's analyze each case mentioned in the question and determine when Q, W, and ΔU are zero.
Case A: Rigid vessel containing steam at 150C left in the atmosphere at 25C
In this case, the vessel is rigid, meaning it does not allow any volume change. Since the vessel is in contact with the atmosphere, it can exchange heat with the surroundings. However, since the temperatures are different, there will be a heat transfer from the steam to the atmosphere until both reach thermal equilibrium. Therefore, in this case, Q is not zero.
Case B: 1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards
In this scenario, the cylinder is insulated, meaning there is no heat transfer with the surroundings. The gas is expanding slowly, which implies that the process is quasi-static. In a quasi-static expansion, the work done is given by the equation W = PΔV, where P is the pressure and ΔV is the change in volume. Since the gas is expanding, ΔV is positive, and the work done will also be positive. Therefore, in this case, W is not zero.
Case C: Rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel
In this case, the vessel, the valve, and the connecting pipes are well insulated. The valve is opened, allowing the ammonia gas to expand into the evacuated vessel. Initially, there is a pressure difference between the two vessels, but as the gas expands, it fills the evacuated vessel until the pressures become equal. Since the vessels and the connecting pipes are well insulated, there is no heat transfer with the surroundings. Additionally, since the process is adiabatic, there is no work done by or on the gas. Therefore, in this case, both Q and W are zero.
Case D: 1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle
In this scenario, the air is flowing adiabatically, meaning there is no heat transfer with the surroundings. The process is also reversible, so there is no work done by or on the air. Therefore, in this case, both Q and W are zero.
Conclusion
Among the given scenarios, only in case C, a rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, are Q, W, and ΔU all zero. This is because the process is adiabatic (no heat transfer), there is no work done, and the change in internal energy is also zero.
Heat transfer (Q), work done (W), and change in internal energy (ΔU) are all related to the energy exchange in a system. In different scenarios, one or more of these quantities may be zero. Let's analyze each case mentioned in the question and determine when Q, W, and ΔU are zero.
Case A: Rigid vessel containing steam at 150C left in the atmosphere at 25C
In this case, the vessel is rigid, meaning it does not allow any volume change. Since the vessel is in contact with the atmosphere, it can exchange heat with the surroundings. However, since the temperatures are different, there will be a heat transfer from the steam to the atmosphere until both reach thermal equilibrium. Therefore, in this case, Q is not zero.
Case B: 1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards
In this scenario, the cylinder is insulated, meaning there is no heat transfer with the surroundings. The gas is expanding slowly, which implies that the process is quasi-static. In a quasi-static expansion, the work done is given by the equation W = PΔV, where P is the pressure and ΔV is the change in volume. Since the gas is expanding, ΔV is positive, and the work done will also be positive. Therefore, in this case, W is not zero.
Case C: Rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel
In this case, the vessel, the valve, and the connecting pipes are well insulated. The valve is opened, allowing the ammonia gas to expand into the evacuated vessel. Initially, there is a pressure difference between the two vessels, but as the gas expands, it fills the evacuated vessel until the pressures become equal. Since the vessels and the connecting pipes are well insulated, there is no heat transfer with the surroundings. Additionally, since the process is adiabatic, there is no work done by or on the gas. Therefore, in this case, both Q and W are zero.
Case D: 1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle
In this scenario, the air is flowing adiabatically, meaning there is no heat transfer with the surroundings. The process is also reversible, so there is no work done by or on the air. Therefore, in this case, both Q and W are zero.
Conclusion
Among the given scenarios, only in case C, a rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, are Q, W, and ΔU all zero. This is because the process is adiabatic (no heat transfer), there is no work done, and the change in internal energy is also zero.
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The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. Can you explain this answer?
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The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. 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 The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. 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 The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. Can you explain this answer?.
The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. 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 The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. 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 The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. Can you explain this answer?.
Solutions for The heat transfer, Q, the work done W and the change in internal energy U are all zero in the case ofa)A rigid vessel containing steam at 150°C left in the atmosphere which is at 25°C.b)1 kg of gas contained in an insulated cylinder expanding as the piston moves slowly outwards.c)A rigid vessel containing ammonia gas connected through a valve to an evacuated rigid vessel, the vessel, the valve and the connecting pipes being well insulated and the valve being opened and after a time, conditions through the two vessels becoming uniform.d)1 kg of air flowing adiabatically from the atmosphere into a previously evacuated bottle.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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