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. If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.?
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. If the pressure of a gas increases by 3 times, then its density beco...
Pressure and Density Relationship:
The pressure of a gas is directly proportional to its density. When the pressure of a gas increases, its density also increases. Mathematically, this relationship can be expressed as:
P ∝ ρ
where P is the pressure and ρ is the density of the gas.
Given Information:
- The pressure of the gas increases by 3 times.
- A box of volume 'V' is connected to another empty vacuumed box of volume '2V' by a tube of negligible volume.
Pressure Exerted by the Gas in the System:
To find the pressure exerted by the gas in the system, let's consider the initial pressure in the box of volume 'V' as P1 and the final pressure after the increase as P2.
Using the Pressure and Density Relationship:
From the given information, we know that the pressure of a gas is directly proportional to its density. Therefore, when the pressure increases by 3 times, the density also increases by the same factor.
Mathematically, if the initial density of the gas is ρ1, the final density after the increase will be ρ2 = 3ρ1.
Using the Relationship between Density and Volume:
Density is defined as the mass per unit volume. Therefore, for a given mass of gas, the density is inversely proportional to the volume it occupies.
Mathematically, if the initial volume of the gas is V1 and the final volume after the increase is V2, then ρ1/V1 = ρ2/V2.
In this case, the initial volume is V and the final volume is 2V. Therefore, ρ1/V = ρ2/(2V).
Substituting the Values:
From the previous calculation, we have ρ2 = 3ρ1. Substituting this value into the equation, we get ρ1/V = (3ρ1)/(2V).
Simplifying the Equation:
Canceling out ρ1 and V from both sides of the equation, we get 1/V = 3/(2V).
Final Calculation:
Simplifying further, we get 2V = 3V. Dividing both sides of the equation by V, we get 2 = 3.
Therefore, the pressure exerted by the gas in the system is 3 times the original pressure.
The pressure of a gas is directly proportional to its density. When the pressure of a gas increases, its density also increases. Mathematically, this relationship can be expressed as:
P ∝ ρ
where P is the pressure and ρ is the density of the gas.
Given Information:
- The pressure of the gas increases by 3 times.
- A box of volume 'V' is connected to another empty vacuumed box of volume '2V' by a tube of negligible volume.
Pressure Exerted by the Gas in the System:
To find the pressure exerted by the gas in the system, let's consider the initial pressure in the box of volume 'V' as P1 and the final pressure after the increase as P2.
Using the Pressure and Density Relationship:
From the given information, we know that the pressure of a gas is directly proportional to its density. Therefore, when the pressure increases by 3 times, the density also increases by the same factor.
Mathematically, if the initial density of the gas is ρ1, the final density after the increase will be ρ2 = 3ρ1.
Using the Relationship between Density and Volume:
Density is defined as the mass per unit volume. Therefore, for a given mass of gas, the density is inversely proportional to the volume it occupies.
Mathematically, if the initial volume of the gas is V1 and the final volume after the increase is V2, then ρ1/V1 = ρ2/V2.
In this case, the initial volume is V and the final volume is 2V. Therefore, ρ1/V = ρ2/(2V).
Substituting the Values:
From the previous calculation, we have ρ2 = 3ρ1. Substituting this value into the equation, we get ρ1/V = (3ρ1)/(2V).
Simplifying the Equation:
Canceling out ρ1 and V from both sides of the equation, we get 1/V = 3/(2V).
Final Calculation:
Simplifying further, we get 2V = 3V. Dividing both sides of the equation by V, we get 2 = 3.
Therefore, the pressure exerted by the gas in the system is 3 times the original pressure.
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. If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.?
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. If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about . If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.?.
. If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about . If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . If the pressure of a gas increases by 3 times, then its density becomes _____A box of volume ‘V’ having gas at pressure ‘P’ is connected to another empty vaccumed box of volume ‘2V’ by a tube of negligible volume. Find the pressure exerted by the gas in the system._ times the original.?.
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