Question

According to Charles’ law:
A) \[\left( {dV/dT} \right){_p}{\text{ }} = {\text{ }}K\]
B) \[\left( {dV/dT} \right){\text{ }}{_p} = - {\text{ }}K\]
C) \[\left( {dV/dT} \right){\text{ }}{_p} = - \dfrac{K}{T}\]
D) None of these

Answer 1

Hint: Charles law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure. The law also states that the Kelvin temperature and the volume will be in direct proportion when the pressure exerted on a sample of a dry gas is held constant.

Complete step by step answer: As per question first we understand the Charles law, It was formulated in the year, \[1780\] by French physicist Jacques Charles, Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is: the volume of an ideal gas at constant pressure is directly proportional to the absolute temperature.
This relationship of direct proportion can be written as-
 \[V \propto T\]

So this means:
\[\dfrac{V}{K} = {\text{ }}T\]
\[\Rightarrow V = KT\]
\[\Rightarrow K{\text{ }} = \dfrac{V}{T}\]
\[\therefore \left( {dV/dT} \right){\text{ }}{_p} = K\]
 where .
\[V\] = volume of the gas,
\[T\;\] = temperature of the gas (measured in Kelvin)
\[K\] = non-zero constant,
\[P\] = Pressure

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. When the temperature changes one unit of the
Kelvin scale equals a change in one Celsius degree. Always remember that zero on the Kelvin
scale means, the unit of temperature must be in Kelvin not in Celsius or Fahrenheit for solving the problems related to Charle’s law.

Hence, option (A) is correct.

Note: charles' law has applied in cold weather or in a cold environment, helium balloons shrink. When the weather is cool, the capacity of the human’s lung decreases. This makes the athletes more difficult to perform on a freezing winter day.