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Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?
- a)1 : 2
- b)1 : 3
- c)1 : 6
- d)3 : 1
Correct answer is option 'C'. Can you explain this answer?
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Two vessels connected by a valve of negligible volume. One container (...
Understanding the Setup
In the given problem, we have two vessels connected by a valve. Let's denote:
- Container I: Contains 2.8 g of N2 gas at temperature T1.
- Container II: Initially evacuated (no gas).
The volume of vessel I is half that of vessel II.
Temperature Conditions
- Container I (T1): Heated to T2 (K).
- Container II: Maintained at T2 / 3 (K).
Gas Behavior and Ideal Gas Law
Using the Ideal Gas Law, the amount of gas in each container can be expressed as:
- \( PV = nRT \)
Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Moles of gas
- \( R \) = Universal gas constant
- \( T \) = Temperature in Kelvin
Volume Consideration
Let:
- Volume of container I = V
- Volume of container II = 2V
Calculating Moles of N2 in Each Container
1. Container I (after heating to T2):
- Moles of N2:
\[
n_I = \frac{P \cdot V}{R \cdot T2}
\]
2. Container II (at T2 / 3):
- Moles of N2 after valve opens:
\[
n_{II} = \frac{P \cdot 2V}{R \cdot (T2/3)} = \frac{6PV}{RT2}
\]
Weight Calculation
Weight of N2 in each container can be calculated as follows:
- Weight in container I (WI):
\[
W_I = n_I \cdot M_{N2} = \frac{P \cdot V \cdot M_{N2}}{R \cdot T2}
\]
- Weight in container II (WII):
\[
W_{II} = n_{II} \cdot M_{N2} = \frac{6PV \cdot M_{N2}}{RT2}
\]
Weight Ratio (WI/WII)
Calculating the weight ratio:
\[
\frac{W_I}{W_{II}} = \frac{\frac{PV}{RT2}}{\frac{6PV}{RT2}} = \frac{1}{6}
\]
Thus, the weight ratio of N2 in both vessels:
\[
W_I : W_{II} = 1 : 6
\]
Conclusion
The correct option is (c) 1 : 6.
In the given problem, we have two vessels connected by a valve. Let's denote:
- Container I: Contains 2.8 g of N2 gas at temperature T1.
- Container II: Initially evacuated (no gas).
The volume of vessel I is half that of vessel II.
Temperature Conditions
- Container I (T1): Heated to T2 (K).
- Container II: Maintained at T2 / 3 (K).
Gas Behavior and Ideal Gas Law
Using the Ideal Gas Law, the amount of gas in each container can be expressed as:
- \( PV = nRT \)
Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Moles of gas
- \( R \) = Universal gas constant
- \( T \) = Temperature in Kelvin
Volume Consideration
Let:
- Volume of container I = V
- Volume of container II = 2V
Calculating Moles of N2 in Each Container
1. Container I (after heating to T2):
- Moles of N2:
\[
n_I = \frac{P \cdot V}{R \cdot T2}
\]
2. Container II (at T2 / 3):
- Moles of N2 after valve opens:
\[
n_{II} = \frac{P \cdot 2V}{R \cdot (T2/3)} = \frac{6PV}{RT2}
\]
Weight Calculation
Weight of N2 in each container can be calculated as follows:
- Weight in container I (WI):
\[
W_I = n_I \cdot M_{N2} = \frac{P \cdot V \cdot M_{N2}}{R \cdot T2}
\]
- Weight in container II (WII):
\[
W_{II} = n_{II} \cdot M_{N2} = \frac{6PV \cdot M_{N2}}{RT2}
\]
Weight Ratio (WI/WII)
Calculating the weight ratio:
\[
\frac{W_I}{W_{II}} = \frac{\frac{PV}{RT2}}{\frac{6PV}{RT2}} = \frac{1}{6}
\]
Thus, the weight ratio of N2 in both vessels:
\[
W_I : W_{II} = 1 : 6
\]
Conclusion
The correct option is (c) 1 : 6.
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Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer?
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Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. 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 Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer?.
Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. 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 Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer?.
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Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two vessels connected by a valve of negligible volume. One container (I) has 2.8 g of N2 at temperature T1(K). The other container (II) is completely evacuated. The container (I) is heated to T2(K) while container (II) is maintained at T2 / 3 (K). Volume of vessel (I) is half that of vessel (II). If the valve is opened then what is the weight ratio of N2 in both vessel (WI / WII)?a)1 : 2b)1 : 3c)1 : 6d)3 : 1Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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