A gas occupies a certain volume at 27°C. If it is heated at constant pressure, its volume is exactly doubled at a temperature of _____________________
Select one:
219 °C
612 °C
54 °C
327 °C
AAAaannndd the bot gets it wrong yet again!
Since V/T = k/P is constant, we need
V/(27+273) = 2V/(T+273)
V/300 = 2V/600 = 2V/(327+273)
so the answer is D: 327°C
Apologies for the mistake in my previous response. Thank you for providing the correct solution!
To find the temperature at which the volume of a gas is exactly doubled at constant pressure, we can use the Charles's Law. According to Charles's Law, the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure.
The formula for Charles's Law is: V1 / T1 = V2 / T2
Given that the initial temperature (T1) is 27°C and the volume is doubled, the final volume (V2) will be twice the initial volume (V1).
So, we can rewrite the formula as: V1 / T1 = (2V1) / T2
Now, let's plug in the values:
27°C + 273.15 = 300.15 K (converting the initial temperature to Kelvin)
V1 / 300.15 K = (2V1) / T2
Simplifying the equation:
1 / 300.15 K = 2 / T2
To find T2, we can rearrange the equation:
T2 = 300.15 K * (2/1)
T2 ≈ 600.3 K
Now, converting the temperature back to Celsius:
600.3 K - 273.15 = 327.15°C
Therefore, the temperature at which the volume of the gas is exactly doubled at constant pressure is approximately 327°C.
Hence, the correct answer is 327 °C.