Question

A certain volume of the gas is kept as 77°C. When the temperature is decreased by 20°C the gas occupies a volume of 900 ml. What was the initial volume of the gas? [pressure constant]

Answer 1

Let
$V_1\mathrm{be}\mathrm{the}\mathrm{initial}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{gas}=x{T}_1\mathrm{be}\mathrm{the}\mathrm{initial}\mathrm{temperature}\mathrm{of}\mathrm{the}\mathrm{gas}\mathrm{in}K=273+77=350K{V}_2\mathrm{be}\mathrm{the}\mathrm{final}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{gas}=900\mathrm{ml}{T}_2\mathrm{be}\mathrm{the}\mathrm{final}\mathrm{temperature}\mathrm{of}\mathrm{the}\mathrm{gas}\mathrm{in}K=330K$


By Charles law
$\frac{V_1}{T_1}=\frac{V_2}{T_2}\mathrm{Substituting}\mathrm{the}\mathrm{values}:\frac{x}{350}=\frac{900}{330}\therefore V_1=\frac{350}{330}\times 900=954.54\mathrm{ml}.\mathrm{Therefore}\mathrm{the}\mathrm{initial}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{gas}\mathrm{is}954.54\mathrm{ml}.$