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Volume of an ideal gas is to be decreased by 10% by increase of pressure by x% under isothermal condition. Thus, x is
- a)100/9
- b)9/100
- c)10
- d)1/10
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Volume of an ideal gas is to be decreased by 10% by increase of pressu...
Applying Boyle 's law P1V1=P2V2 as temp is constant.
So let initial pressure =P initial volume =V
Now final volume V2=V-10%of V =9V/10
PV=P2×9V/10 so P2=10P/9
Therefore increment in Pressure=P/9P×100%=100/9
So let initial pressure =P initial volume =V
Now final volume V2=V-10%of V =9V/10
PV=P2×9V/10 so P2=10P/9
Therefore increment in Pressure=P/9P×100%=100/9
Most Upvoted Answer
Volume of an ideal gas is to be decreased by 10% by increase of pressu...
Apply boyle 's law P1V1=P2V2 as temp is const so let initial pressure =P initial volume =V now final volume V2=V-10%of V =9V/10 now PV=P2×9V/10 so P2=10P/9 so increment in Pressure=P/9P×100%=100/9
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Volume of an ideal gas is to be decreased by 10% by increase of pressu...
To solve this problem, let's consider the ideal gas law, which states that the product of the pressure (P) and volume (V) of an ideal gas is directly proportional to the number of moles (n) and the temperature (T) of the gas. Mathematically, this can be expressed as:
PV = nRT
Where R is the ideal gas constant.
Now, let's assume the initial volume of the gas is V and the initial pressure is P. According to the problem, we need to decrease the volume by 10% and increase the pressure by x%.
1. Decrease in Volume:
The new volume after decreasing it by 10% can be expressed as V - 0.1V = 0.9V.
2. Increase in Pressure:
The new pressure after increasing it by x% can be expressed as P + (x/100)P = (1 + x/100)P.
Since the process is isothermal, the temperature remains constant. Therefore, the product of the initial pressure and volume is equal to the product of the final pressure and volume. Mathematically, this can be expressed as:
PV = (0.9V) * [(1 + x/100)P]
Simplifying the equation, we get:
V = (0.9) * (1 + x/100)
Now, let's solve for x:
V = 0.9 + 0.9x/100
0.9x/100 = V - 0.9
x/100 = (V - 0.9) / 0.9
x = 100 * (V - 0.9) / 0.9
From the equation above, we can see that x is directly proportional to V - 0.9. Since V - 0.9 represents the decrease in volume (10% decrease), we can substitute it with -0.1V. Therefore, x can be rewritten as:
x = 100 * (-0.1V) / 0.9
x = -100/9 * V
Hence, x is equal to -100/9, which is option A in the given choices.
PV = nRT
Where R is the ideal gas constant.
Now, let's assume the initial volume of the gas is V and the initial pressure is P. According to the problem, we need to decrease the volume by 10% and increase the pressure by x%.
1. Decrease in Volume:
The new volume after decreasing it by 10% can be expressed as V - 0.1V = 0.9V.
2. Increase in Pressure:
The new pressure after increasing it by x% can be expressed as P + (x/100)P = (1 + x/100)P.
Since the process is isothermal, the temperature remains constant. Therefore, the product of the initial pressure and volume is equal to the product of the final pressure and volume. Mathematically, this can be expressed as:
PV = (0.9V) * [(1 + x/100)P]
Simplifying the equation, we get:
V = (0.9) * (1 + x/100)
Now, let's solve for x:
V = 0.9 + 0.9x/100
0.9x/100 = V - 0.9
x/100 = (V - 0.9) / 0.9
x = 100 * (V - 0.9) / 0.9
From the equation above, we can see that x is directly proportional to V - 0.9. Since V - 0.9 represents the decrease in volume (10% decrease), we can substitute it with -0.1V. Therefore, x can be rewritten as:
x = 100 * (-0.1V) / 0.9
x = -100/9 * V
Hence, x is equal to -100/9, which is option A in the given choices.
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