Question

When the temperature of air rises by 3K from 300K, what is the percentage rise in the velocity of sound?
(A) 0.5%
(B) 1%
(C) 2%
(D) None of the options

Answer 1

Hint :Temperature is a physical quantity that conveys hot and cold. When a body comes into contact with another that is colder or hotter, it is the manifestation of thermal energy, which is present in all matter and is the cause of the occurrence of heat, a flow of energy. Sound velocity is related to the square root of air temperature. So we use this relation to solve the problem.

Complete Step By Step Answer:
A thermometer is used to determine the temperature. Thermometers are calibrated in a variety of temperature scales that have traditionally defined temperature using a variety of reference points and thermometric substances. The Celsius scale (previously known as centigrade, designated as °C), the Fahrenheit scale (denoted as °F), and the Kelvin scale (denoted as K) are the most prevalent scales. The Kelvin scale (denoted as K) is primarily used for scientific purposes under conventions of the International System of Units (SI). The rate of change of an object's location with regard to a frame of reference is its velocity, which is a function of time. Velocity is the measurement of an object's speed and direction of motion.
$ \Rightarrow {\text{v}} \propto \sqrt {\text{T}} $
So,
$ \Rightarrow \dfrac{{{{\text{v}}^\prime }}}{{\text{v}}} = \sqrt {\dfrac{{{{\text{T}}^\prime }}}{{\text{T}}}} $
Hence, Rise in velocity % is = $\dfrac{{v` - v}}{v} \times 100$
Hence it can be written as
$ = \dfrac{{\sqrt {\dfrac{{{T^\prime }}}{T}} - 1}}{1} \times 100$
\[ = \dfrac{{\sqrt {\dfrac{{303}}{{300}}} - 1}}{1} \times 100\]
$ \Rightarrow \% = 0.5\% $
Hence option A is correct.

Note :
Absolute zero is the lowest theoretical temperature at which no additional thermal energy can be collected from a substance. The third rule of thermodynamics recognises that it can only be approached extremely precisely (100 pK) but not obtained experimentally. Temperature is significant in physics, chemistry, Earth science, astronomy, medicine, biology, ecology, material science, metallurgy, mechanical engineering, and geography, as well as most elements of everyday life.