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A frictionless heat-conducting piston of negligible mass and heat capacity divides a vertical, insulated cylinder of height 2H and cross-sectional area A into two halves. Each half contains one mole of an ideal gas at temperatures T0 and P0 corresponding to STP. The heat capacity ratio γ = Cp/Cv is given. A load of weight W is tied to the piston and suddenly released. After the system comes to equilibrium, the piston is at rest and the temperatures of the gases in the two compartments are equal. What is the final displacement y of the piston from its initial position, assuming yW >> T0Cv.
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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A frictionless heat-conducting piston of negligible mass and heat capa...
We have an insulated cylinder of height 2H and cross-sectional area A.
A piston divides this into 2 equal halves.
Each half contains one mole of an ideal gas at temperatures T0 and P0 corresponding to STP.
heat capacity ratio γ = Cp/Cv .
Due to weight W, there is some displacement let's say it y.
Now from the balance equation we get:
mgy = change in internal energy.
mgy=2Cv(T−T0)
1 mole each in each compartment.
Now;
As PV = nRT and volume of each individual component is given as:
A (H-y) and A (H+y) respectively.
Now simplifying it a bit we get:
Again, we had the relationship,
Now putting the value of T in the above expression we get:
given that Wy >> T0Cv, we get:
We know that Cp−Cv=R.
From this, we can write:
Putting this above expression in the expression above for y we get:
Solving it for y we get:
A piston divides this into 2 equal halves.
Each half contains one mole of an ideal gas at temperatures T0 and P0 corresponding to STP.
heat capacity ratio γ = Cp/Cv .
Due to weight W, there is some displacement let's say it y.
Now from the balance equation we get:
mgy = change in internal energy.
mgy=2Cv(T−T0)
1 mole each in each compartment.
Now;
As PV = nRT and volume of each individual component is given as:
A (H-y) and A (H+y) respectively.
Now simplifying it a bit we get:
Again, we had the relationship,
Now putting the value of T in the above expression we get:
given that Wy >> T0Cv, we get:
We know that Cp−Cv=R.
From this, we can write:
Putting this above expression in the expression above for y we get:
Solving it for y we get:
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A frictionless heat-conducting piston of negligible mass and heat capacity divides a vertical, insulated cylinder of height 2H and cross-sectional area A into two halves. Each half contains one mole of an ideal gas at temperatures T0and P0corresponding to STP. The heat capacity ratioγ = Cp/Cvis given. A load of weight W is tied to the piston and suddenly released. After the system comes to equilibrium, the piston is at rest and the temperatures of the gases in the two compartments are equal. What is the final displacement y of the piston from its initial position, assuming yW >> T0Cv.a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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A frictionless heat-conducting piston of negligible mass and heat capacity divides a vertical, insulated cylinder of height 2H and cross-sectional area A into two halves. Each half contains one mole of an ideal gas at temperatures T0and P0corresponding to STP. The heat capacity ratioγ = Cp/Cvis given. A load of weight W is tied to the piston and suddenly released. After the system comes to equilibrium, the piston is at rest and the temperatures of the gases in the two compartments are equal. What is the final displacement y of the piston from its initial position, assuming yW >> T0Cv.a)b)c)d)Correct answer is option 'B'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about A frictionless heat-conducting piston of negligible mass and heat capacity divides a vertical, insulated cylinder of height 2H and cross-sectional area A into two halves. Each half contains one mole of an ideal gas at temperatures T0and P0corresponding to STP. The heat capacity ratioγ = Cp/Cvis given. A load of weight W is tied to the piston and suddenly released. After the system comes to equilibrium, the piston is at rest and the temperatures of the gases in the two compartments are equal. What is the final displacement y of the piston from its initial position, assuming yW >> T0Cv.a)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A frictionless heat-conducting piston of negligible mass and heat capacity divides a vertical, insulated cylinder of height 2H and cross-sectional area A into two halves. Each half contains one mole of an ideal gas at temperatures T0and P0corresponding to STP. The heat capacity ratioγ = Cp/Cvis given. A load of weight W is tied to the piston and suddenly released. After the system comes to equilibrium, the piston is at rest and the temperatures of the gases in the two compartments are equal. What is the final displacement y of the piston from its initial position, assuming yW >> T0Cv.a)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
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