Answer:
–132.55 °C
Explanation:
From the question given above, the following data were obtained:
Initial volume (V₁) = 30.8 L
Initial temperature (T₁) = –67 °C
Final volume (V₂) = 21.0 L
Final temperature (T₂) =?
Next, we shall convert –67 °C to Kelvin temperature. This can be obtained as follow:
T(K) = T(°C) + 273
Initial temperature (T₁) = –67 °C
Initial temperature (T₁) = –67 °C + 273
Initial temperature (T₁) = 206 K
Next, we shall determine the final temperature of the gas. This can be obtained as follow:
Initial volume (V₁) = 30.8 L
Initial temperature (T₁) = 206 K
Final volume (V₂) = 21.0 L
Final temperature (T₂) =?
V₁/T₁ = V₂/T₂
30.8 / 206 = 21 / T₂
Cross multiply
30.8 × T₂ = 206 × 21
30.8 × T₂ = 4326
Divide both side by 30.8
T₂ = 4326 / 30.8
T₂ = 140.45 K
Finally, we shall convert 140.45 K to celsius temperature. This can be obtained as follow:
T(°C) = T(K) – 273
T₂ = 140.45 K
T₂ = 140.45 K – 273
T₂ = –132.55 °C
Thus, the new temperature of the gas is –132.55 °C
