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A car tyre is slowly pumped up to a pressure of 2 atm in an environment at 150C. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside the tyre to be adiabatic, its temperature (in K) after the burst is ______.
Correct answer is '236.3'. Can you explain this answer?
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Given data:
- Initial pressure inside the car tyre = 2 atm
- Initial temperature inside the car tyre = 150°C
- The burst of the tyre is assumed to be adiabatic
Formula:
The adiabatic process for an ideal gas is given by the equation:
P1 * V1^γ = P2 * V2^γ
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
γ = Adiabatic index (ratio of specific heat capacities)
Solution:
Step 1: Convert the initial temperature to Kelvin:
Initial temperature in Kelvin = 150 + 273.15 = 423.15 K
Step 2: Calculate the initial volume:
Since the volume is not given, we can assume the volume to be constant. Therefore, the initial volume can be considered as V1 = V2.
Step 3: Determine the adiabatic index (γ):
The adiabatic index for a mixture of oxygen (O2) and nitrogen (N2) gases can be estimated as the weighted average of their individual adiabatic indices.
γ = (f1 * γ1 + f2 * γ2) / (f1 + f2)
Where:
γ1 = Adiabatic index for oxygen gas (approximately 1.4)
γ2 = Adiabatic index for nitrogen gas (approximately 1.4)
f1 = Fraction of oxygen gas in the mixture
f2 = Fraction of nitrogen gas in the mixture
Step 4: Substitute the given values into the adiabatic process equation:
P1 * V1^γ = P2 * V2^γ
Since V1 = V2, the equation becomes:
P1 = P2
Therefore,
P1^((γ-1)/γ) = P2^((γ-1)/γ)
Step 5: Solve for the final temperature (T2):
The final temperature can be calculated using the ideal gas equation:
P1 * V1 / T1 = P2 * V2 / T2
Since the volume is constant, the equation becomes:
P1 / T1 = P2 / T2
Therefore,
T2 = T1 * (P2 / P1)
Step 6: Substitute the given values into the equation:
T2 = 423.15 K * (2 atm / 2 atm)
Step 7: Calculate the final temperature:
T2 = 423.15 K
Therefore, the temperature of the air inside the tyre after the burst is 423.15 K, which is approximately 236.3°C.
- Initial pressure inside the car tyre = 2 atm
- Initial temperature inside the car tyre = 150°C
- The burst of the tyre is assumed to be adiabatic
Formula:
The adiabatic process for an ideal gas is given by the equation:
P1 * V1^γ = P2 * V2^γ
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
γ = Adiabatic index (ratio of specific heat capacities)
Solution:
Step 1: Convert the initial temperature to Kelvin:
Initial temperature in Kelvin = 150 + 273.15 = 423.15 K
Step 2: Calculate the initial volume:
Since the volume is not given, we can assume the volume to be constant. Therefore, the initial volume can be considered as V1 = V2.
Step 3: Determine the adiabatic index (γ):
The adiabatic index for a mixture of oxygen (O2) and nitrogen (N2) gases can be estimated as the weighted average of their individual adiabatic indices.
γ = (f1 * γ1 + f2 * γ2) / (f1 + f2)
Where:
γ1 = Adiabatic index for oxygen gas (approximately 1.4)
γ2 = Adiabatic index for nitrogen gas (approximately 1.4)
f1 = Fraction of oxygen gas in the mixture
f2 = Fraction of nitrogen gas in the mixture
Step 4: Substitute the given values into the adiabatic process equation:
P1 * V1^γ = P2 * V2^γ
Since V1 = V2, the equation becomes:
P1 = P2
Therefore,
P1^((γ-1)/γ) = P2^((γ-1)/γ)
Step 5: Solve for the final temperature (T2):
The final temperature can be calculated using the ideal gas equation:
P1 * V1 / T1 = P2 * V2 / T2
Since the volume is constant, the equation becomes:
P1 / T1 = P2 / T2
Therefore,
T2 = T1 * (P2 / P1)
Step 6: Substitute the given values into the equation:
T2 = 423.15 K * (2 atm / 2 atm)
Step 7: Calculate the final temperature:
T2 = 423.15 K
Therefore, the temperature of the air inside the tyre after the burst is 423.15 K, which is approximately 236.3°C.
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A car tyre is slowly pumped up to a pressure of 2 atm in an environment at 150C. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside the tyre to be adiabatic, its temperature (in K) after the burst is ______.Correct answer is '236.3'. Can you explain this answer?
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A car tyre is slowly pumped up to a pressure of 2 atm in an environment at 150C. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside the tyre to be adiabatic, its temperature (in K) after the burst is ______.Correct answer is '236.3'. 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 car tyre is slowly pumped up to a pressure of 2 atm in an environment at 150C. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside the tyre to be adiabatic, its temperature (in K) after the burst is ______.Correct answer is '236.3'. 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 car tyre is slowly pumped up to a pressure of 2 atm in an environment at 150C. At this point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside the tyre to be adiabatic, its temperature (in K) after the burst is ______.Correct answer is '236.3'. Can you explain this answer?.
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