Given :
A sample of unknown gas has a temperature of 378 K.
[tex]T_i = 378 \ K , \ T_f = 546 \ K[/tex]
When the temperature is increased to 546 K, the volume also increases to 1047 ml.
[tex]V_f - V_i = 1047 \ ml[/tex]
Solution :
We know, temperature is directly proportional to volume.
[tex]\dfrac{T_i}{T_f}=\dfrac{V_i}{V_f}\\\\\dfrac{T_i}{T_f} = \dfrac{V_i}{1047 + V_i}\\\\\dfrac{V_i}{1047+V_i}=\dfrac{378}{546}\\\\546V_i = 378V_i + 378\times 1047\\\\168V_i = 3,95,766\\\\V_i = 2,355.75\ ml[/tex]
Therefore, the original volume is 2.355.75 ml.
