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A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).
Correct answer is '92.8'. Can you explain this answer?
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Verified Answer
A thermally isolated container stores gas at 27.240C at one atmospheri...
We know that
P1 = 1 atm
T1 = 300.24 k
P2 = 2 atm
T2 = ?
P1 = 1 atm
T1 = 300.24 k
P2 = 2 atm
T2 = ?
Most Upvoted Answer
A thermally isolated container stores gas at 27.240C at one atmospheri...
Given:
- Initial temperature of the gas (T1) = 27.24°C
- Initial pressure of the gas (P1) = 1 atmospheric pressure
- Final pressure of the gas (P2) = 2 atmospheric pressures
To find:
Change in temperature of the gas (T2 - T1)
Assumptions:
- The gas behaves as an ideal gas, following the ideal gas law.
- The container is thermally isolated, meaning no heat is exchanged with the surrounding.
Solution:
The ideal gas law states that:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature in Kelvin
Since the volume and number of moles of gas remain constant, we can rewrite the equation as:
P/T = constant
Step 1: Convert temperatures to Kelvin
Since the ideal gas law requires temperature to be in Kelvin, we need to convert the given temperatures from Celsius to Kelvin.
T1 = 27.24 + 273.15 = 300.39 K
Step 2: Calculate the initial temperature using the ideal gas law
Using the initial pressure and temperature, we can find the constant:
P1/T1 = constant
Step 3: Calculate the final temperature using the ideal gas law
Using the final pressure and the constant obtained in step 2:
P2/T2 = constant
Step 4: Solve for T2
Rearranging the equation in step 3, we get:
T2 = P2 * (T1/P1)
Plugging in the given values:
T2 = 2 * (300.39/1) = 600.78 K
Step 5: Convert the final temperature to Celsius
Finally, we need to convert the final temperature from Kelvin to Celsius:
T2 - 273.15 = 600.78 - 273.15 = 327.63°C
Step 6: Calculate the change in temperature
Change in temperature = T2 - T1
Change in temperature = 327.63 - 27.24 = 300.39°C
Therefore, the change in temperature of the gas is approximately 300.39°C.
- Initial temperature of the gas (T1) = 27.24°C
- Initial pressure of the gas (P1) = 1 atmospheric pressure
- Final pressure of the gas (P2) = 2 atmospheric pressures
To find:
Change in temperature of the gas (T2 - T1)
Assumptions:
- The gas behaves as an ideal gas, following the ideal gas law.
- The container is thermally isolated, meaning no heat is exchanged with the surrounding.
Solution:
The ideal gas law states that:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature in Kelvin
Since the volume and number of moles of gas remain constant, we can rewrite the equation as:
P/T = constant
Step 1: Convert temperatures to Kelvin
Since the ideal gas law requires temperature to be in Kelvin, we need to convert the given temperatures from Celsius to Kelvin.
T1 = 27.24 + 273.15 = 300.39 K
Step 2: Calculate the initial temperature using the ideal gas law
Using the initial pressure and temperature, we can find the constant:
P1/T1 = constant
Step 3: Calculate the final temperature using the ideal gas law
Using the final pressure and the constant obtained in step 2:
P2/T2 = constant
Step 4: Solve for T2
Rearranging the equation in step 3, we get:
T2 = P2 * (T1/P1)
Plugging in the given values:
T2 = 2 * (300.39/1) = 600.78 K
Step 5: Convert the final temperature to Celsius
Finally, we need to convert the final temperature from Kelvin to Celsius:
T2 - 273.15 = 600.78 - 273.15 = 327.63°C
Step 6: Calculate the change in temperature
Change in temperature = T2 - T1
Change in temperature = 327.63 - 27.24 = 300.39°C
Therefore, the change in temperature of the gas is approximately 300.39°C.
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A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer?
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A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer?.
A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermally isolated container stores gas at 27.240C at one atmospheric pressure. Suddenly the pressure of the gas is increased to two atmospheric pressures. Assuming N2, to behave as an ideal gas, estimate the change in temperature of the gas, in Celsius degrees (0C).Correct answer is '92.8'. Can you explain this answer?.
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