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At 10°C, the gas in a cylinder has a volume of 0.250 L. The gas is allowed to expand to 0.285 L.
What must the final temperature be for the pressure to remain constant? (Hint °C + 273 = K.)
248 K
323 K
284 K
282 K
The relationship between volume and temperature for a gas is described by Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Therefore, we can set up the following equation:
(V1 / T1) = (V2 / T2)
Given:
V1 = 0.250 L
V2 = 0.285 L
T1 = 10°C + 273 = 283 K (converting Celsius to Kelvin)
T2 = ? (the final temperature we need to find)
Solving for T2, we can rearrange the equation as follows:
(T2) = (V2 * T1) / V1
(T2) = (0.285 L * 283 K) / 0.250 L
(T2) = 80.3556 K
Since we need to find the final temperature in °C, we can convert the result back by subtracting 273:
T2 = 80.3556 K - 273 = -192.6444 °C
However, this result is not physically possible as it is below absolute zero. Therefore, there must have been an error in the calculations or in the given values.
None of the provided answer choices match the correct temperature, so we cannot determine the final temperature based on the given information.