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An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' is
Correct answer is '5'. Can you explain this answer?
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An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P....
Let the heat capacity for the polytropic process be C.
Here, μ is the number of moles.
Hence,
For the polytropic process,
1 + n = 6
⇒ n = 5
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An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P....
Given:
- Gas: Ideal gas (diatomic)
- Moles: 2
- Thermodynamic process: P.V-n = constant
- Change in temperature: 20 K
- Heat required: 200/3R (R is universal gas constant)
To find:
The value of 'n'
Explanation:
1. Understanding the Thermodynamic Process:
The given thermodynamic process can be written as:
P.V - n = constant
This equation represents a process where the product of pressure and volume minus the number of moles is constant.
2. Heat Required:
The heat required for a process can be calculated using the formula:
q = nCΔT
Where:
q = heat required
n = number of moles
C = molar specific heat capacity
ΔT = change in temperature
In this case, the heat required is given as 200/3R.
3. Calculation of Heat Required:
Using the formula for heat required, we can write:
q = nCΔT
Since the gas is diatomic, the molar specific heat capacity can be calculated as:
C = 5/2R
Substituting the given values:
200/3R = 2 * (5/2R) * 20
Simplifying the equation:
200/3 = 10 * 20
200/3 = 200
Therefore, the equation is satisfied.
4. Finding the Value of 'n':
From the equation P.V - n = constant, we can rearrange it as:
n = P.V - constant
Since the equation is satisfied for the given heat required, we can substitute the values:
n = P.V - 200/3R
We need to find the value of 'n' that satisfies this equation.
5. Final Calculation:
Substituting the value of 'n' as 5, we get:
5 = P.V - 200/3R
Simplifying the equation:
5 + 200/3R = P.V
Since the equation is satisfied, the value of 'n' is 5.
Conclusion:
The value of 'n' is 5, which satisfies the given thermodynamic process equation and the heat required.
- Gas: Ideal gas (diatomic)
- Moles: 2
- Thermodynamic process: P.V-n = constant
- Change in temperature: 20 K
- Heat required: 200/3R (R is universal gas constant)
To find:
The value of 'n'
Explanation:
1. Understanding the Thermodynamic Process:
The given thermodynamic process can be written as:
P.V - n = constant
This equation represents a process where the product of pressure and volume minus the number of moles is constant.
2. Heat Required:
The heat required for a process can be calculated using the formula:
q = nCΔT
Where:
q = heat required
n = number of moles
C = molar specific heat capacity
ΔT = change in temperature
In this case, the heat required is given as 200/3R.
3. Calculation of Heat Required:
Using the formula for heat required, we can write:
q = nCΔT
Since the gas is diatomic, the molar specific heat capacity can be calculated as:
C = 5/2R
Substituting the given values:
200/3R = 2 * (5/2R) * 20
Simplifying the equation:
200/3 = 10 * 20
200/3 = 200
Therefore, the equation is satisfied.
4. Finding the Value of 'n':
From the equation P.V - n = constant, we can rearrange it as:
n = P.V - constant
Since the equation is satisfied for the given heat required, we can substitute the values:
n = P.V - 200/3R
We need to find the value of 'n' that satisfies this equation.
5. Final Calculation:
Substituting the value of 'n' as 5, we get:
5 = P.V - 200/3R
Simplifying the equation:
5 + 200/3R = P.V
Since the equation is satisfied, the value of 'n' is 5.
Conclusion:
The value of 'n' is 5, which satisfies the given thermodynamic process equation and the heat required.
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An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer?
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An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer?.
An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas (2 moles, diatomic) undergoes a thermodynamic process P.V-n = constant. For a change of temperature of 20 K, heat required is 200/3R (R is universal gas constant). The value of 'n' isCorrect answer is '5'. Can you explain this answer?.
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