Question

400 cm³ of hydrogen is at normal temperature. Find the temperature of gas for the following volume when pressure remains constant.

150 cm³

Answer 1

Step-1: Understand the given conditions

• Pressure is constant.
• Volume of Hydrogen = $400{\mathrm{cm}}^3$
• Temperature of Hydrogen= Normal temperature
• The value of normal temperature= $273\mathrm{K}$
• Temperature to be calculated at $150{\mathrm{cm}}^3$

Step-2: Apply Charles' law equation to find out the temperature at the given volume of $150{\mathrm{cm}}^3$

Charles' law: According to Charles' law, at constant pressure, volume is directly proportional to temperature for a given mass of the gas.
or $\frac{\mathrm{V}}{\mathrm{T}}=\mathrm{constant}$

Therefore, for two different conditions i.e. 1 and 2, Charles' law can be written as:
$\frac{{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{V}}_2}{{\mathrm{T}}_2}$

• Let the volume of Hydrogen at temperature $273\mathrm{K}$= ${\mathrm{V}}_1$i.e.; $400{\mathrm{cm}}^3$
• Let the temperature of Hydrogen at volume ${\mathrm{V}}_1$= ${\mathrm{T}}_1$i.e.; $273\mathrm{K}$
• Let the volume of Hydrogen at temperature ${\mathrm{T}}_2$= ${\mathrm{V}}_2$ i.e.; $150{\mathrm{cm}}^3$
• Let the temperature of Hydrogen at volume $150{\mathrm{cm}}^3$= i.e.; ${\mathrm{T}}_2$ (to be calculated)

Substituting the values in the above equation

$$\begin{gathered} \frac{400}{273}=\frac{150}{{\mathrm{T}}_2} \\ {\mathrm{T}}_2=\frac{150\times 273}{400} \\ {\mathrm{T}}_2=\frac{40950}{400}=102.375\mathrm{K} \end{gathered}$$

${\mathrm{T}}_2=102.375\mathrm{K}$

Step-3: Conversion to degrees Celsius

$\mathrm{Temperature}\mathrm{in}°\mathrm{C}+273=\mathrm{Temperature}\mathrm{in}\mathrm{K}$

Therefore, to convert $102.375\mathrm{K}$ to degree Celsius, subtract 273 from it as shown below

$102.375-273=-170.62°\mathrm{C}$

So, ${\mathrm{T}}_2=102.375\mathrm{K}\mathrm{or}-170.62°\mathrm{C}$