Question

A sample of gas occupies \[{\text{100 mL}}\]at \[27^\circ {\text{C}}\] and \[{\text{740 mm}}\] pressure. When its volume is changed to \[{\text{80 mL}}\] at \[{\text{740 mm}}\] pressure, the temperature of the gas will be:
A ) \[21.6^\circ {\text{C}}\]
B ) \[240^\circ {\text{C}}\]
C ) \[ - 33^\circ {\text{C}}\]
D ) \[89.5^\circ {\text{C}}\]

Answer 1

Hint: According to Charle’s law, for a fixed number of moles of an ideal gas, at constant pressure, the volume is directly proportional to the absolute temperature.
\[\dfrac{{{V_1}}}{{{V_2}}} = \dfrac{{{T_1}}}{{{T_2}}}\]

Complete step by step answer:
Write the ideal gas equation:
\[PV = nRT\]
Here, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant and T is absolute temperature.
Let \[{V_1},{T_1}\] be the initial volume and initial temperature. \[{V_2},{T_2}\] are the final volume and final temperature respectively.
According to Charle’s law, for a fixed number of moles of an ideal gas, at constant pressure, the volume is directly proportional to the absolute temperature.
\[{\text{V}} \propto {\text{T}} \\
\dfrac{{{V_1}}}{{{V_2}}} = \frac{{{T_1}}}{{{T_2}}} \\
{T_2} = {T_1} \times \dfrac{{{V_2}}}{{{V_1}}} \\\]
The initial volume and the initial temperature are \[{\text{100 mL}}\] and \[27^\circ {\text{C}}\] respectively.
The final volume is \[{\text{80 mL}}\].
Substitute values in the above equation and calculate the final temperature:
\[{T_2} = {T_1} \times \dfrac{{{V_2}}}{{{V_1}}} \\
= \left( {27 + 273} \right){\text{ K}} \times \dfrac{{80{\text{ mL}}}}{{100{\text{ mL}}}} \\
= 240{\text{ K}} \\\]
Hence, the final temperature is \[240{\text{ K}}\]. Convert the unit from kelvin to degree celsius by subtracting 273.
\[ {T_2} = 240 - 273{\text{ }}^\circ {\text{C}} \\
= - 33{\text{ }}^\circ {\text{C}} \\\]
Hence, the final temperature is \[ - 33^\circ {\text{C}}\] .

Hence, the correct option is the option C ) \[ - 33^\circ {\text{C}}\].

Note: Do not substitute the value of temperature in the unit of degree celsius in the equation. Convert the unit from degree celsius to kelvin by adding 273. In this question, the number of moles of the ideal gas and pressure are constant. But the volume of gas and its temperature change.