Question

Consider a 1 c.c. sample of air at absolute temperature $\mathrm{T}_{0}$ at sea level and another 1c.c. sample of air at a height where the pressure is one-third atmosphere. The absolute temperature T of the sample at the height is:
A. Equal to \[\dfrac{{{T}_{0}}}{3}\]
B. Equal to $\dfrac{3}{{{T}_{0}}}$
C. Equal to \[{{T}_{0}}\]
D. Cannot be determined in terms of \[{{T}_{0}}\] from the above data

Answer 1

Hint: The temperature of an object on a scale where 0 is taken as absolute zero is the absolute temperature, also called thermodynamic temperature. Kelvin (Celsius degree units) and Rankine (Fahrenheit degree units) are absolute temperature scales. Calculate Initial pressure , Initial temperature Then find out Final pressure by A relation between Pressure and temperature.

Complete step by step solution:
Absolute temperature is defined as a temperature measurement starting on the Kelvin scale at absolute zero. In the thermodynamics study, an example of when one could use absolute temperature as a form of measurement. STP condition is defined (as per the International Standard Metric Conditions) as the surrounding absolute temperature of 288.15 Kelvin $\left( {{15}^{{}^\circ }} \right.C)$ and a pressure of 1 atmosphere i.e. 1 bar or \[101.325\text{ }Kpa.\]
According to the question. The given data
Let the initial pressure be $\mathrm{P}_{0}$
Let the initial temperature be $\mathrm{T}_{0}$ It is given that final pressure $\mathrm{P}_{1}=\dfrac{\mathrm{P}_{0}}{3}$
So, we know the relation $\mathrm{P} \propto \mathrm{T}$
Hence $\dfrac{\mathrm{P}_{0}}{\mathrm{T}_{0}}=\dfrac{\mathrm{P}_{0}}{3 \mathrm{T}}$
$\therefore \text{T}=\dfrac{{{\text{T}}_{0}}}{3}$
The absolute temperature T of the sample at the height is $\dfrac{{{\text{T}}_{0}}}{3}$

Hence, the correct option is (A).

Note:
It appeared that at what is now called the absolute zero of temperature, a "ideal gas" at constant pressure would reach zero volume. Actually, any real gas condenses to a liquid or a solid at a temperature above absolute zero at some temperature. Therefore, only an approximation to real gas behavior is the ideal gas law. The measure of gas volume and pressure is the absolute temperature of a gas. Because it has been discovered that at absolute zero