Question

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

Volume increases by 800 %

Answer 1

Step 1: Analyzing the given data

Initial condition:

T₁ = Normal temperature = 273 K

V₁ = 400 cm³

Final condition:

T₂ = ?

When volume increases by 800%

Increase in the volume=$\frac{800}{100}{\mathrm{V}}_1$

Final volume ${\mathrm{V}}_2={\mathrm{V}}_1+\frac{800}{100}{\mathrm{V}}_1$

Substituting the value of ${\mathrm{V}}_1$as $400{\mathrm{cm}}^3$ in the above equation

${\mathrm{V}}_2=400+\frac{800}{100}\times 400$

${\mathrm{V}}_2=400+3200=3600{\mathrm{cm}}^3$

Step 2: Calculating the final temperature of gas

Since, the pressure remains constant, according to Charle's law temperature of a gas is directly proportional to the volume of gas.

Formula : $\frac{{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{V}}_2}{{\mathrm{T}}_2}$

$$\begin{gathered} \frac{400{\mathrm{cm}}^3}{273\mathrm{K}}=\frac{3600{\mathrm{cm}}^3}{{\mathrm{T}}_2} \\ {\mathrm{T}}_2=\frac{3600\times 273}{400}\mathrm{K} \\ {\mathrm{T}}_2=\frac{982800}{400}=2457\mathrm{K} \end{gathered}$$

Thus, the final temperature is 2457 K.