Question:

At constant temperature, the volume of a gas is to be decreased by 4%. The pressure must be increased by

Updated On: Jul 6, 2022
  • 0.04
  • 0.0416
  • 0.08
  • 0.0386
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The Correct Option is B

Solution and Explanation

At constant temperature, $ p_1 V_1 = p_2 V_2 $ $\Rightarrow \frac{ p_1 }{ p_2 } = \frac{ V_2 }{ V_1 } $ Hence fractional change in volume $\Rightarrow \frac{ V_1 - V_2 }{ V_1 } = \frac{ 4 }{ 100} = \frac{ 1}{ 25 } $ $\Rightarrow 1 - \frac{ V_2 }{ V_1 } = \frac{ 1}{25} $ $\Rightarrow \frac{ V_2 }{ V_1 } = \frac{ 24}{25} $ $\Rightarrow \frac{ p_1 }{ p_2 } = \frac{ V_2 }{ V_1 } = \frac{ 24}{25} $ $\Rightarrow \frac{ p_2 - p_! }{ p_1 } = \frac{ 24}{25} - 1 = \frac{ 1}{ 24 }$ Percentage increase in pressure = $ \frac{ 100}{ 24} = $ 4.16%.
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Notes on Units and measurement

Concepts Used:

Units and Measurement

Unit:

A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.

Measurement:

The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.

Read More: Fundamental and Derived Units of Measurement

System of Units:

  1. CGS system
  2. FPS system
  3. MKS system
  4. SI units

Types of Units:

Fundamental Units -

The units defined for the fundamental quantities are called fundamental units.

Derived Units -

The units of all other physical quantities which are derived from the fundamental units are called the derived units.