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The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.
What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?
(Rounded off to the nearest integer)
Correct answer is '26'. Can you explain this answer?
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Most Upvoted Answer
The pressure in an automobile tire depends on the temperature of the ...
Initially, the absolute pressure in the tire is
P1 = Pg + Patm = 210 + 100 = 310 kPa
Treating air as an ideal gas and assuming the volume of the tire to remain constant, the final pressure in the tire can be determined from
Thus the pressure rise is
ΔP = P2 - P1 = 336 - 310 = 26 kPa
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Community Answer
The pressure in an automobile tire depends on the temperature of the ...
Given:
Temperature of air in the tire (T1) = 25°C
Pressure reading on the gauge (P1) = 210 kPa
Volume of the tire (V) = 0.025 m3
Atmospheric pressure (P0) = 100 kPa
Temperature of air in the tire after rise (T2) = 50°C
Target:
To calculate the rise in pressure in the tire when the air temperature rises to 50°C.
Assumptions:
1. The tire is considered to be a closed system.
2. The ideal gas law is applicable.
3. The tire is assumed to be rigid and impermeable.
Explanation:
The ideal gas law equation is given by:
PV = nRT
Where,
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature
Step 1: Calculate the initial number of moles of gas in the tire.
To calculate the number of moles, we can rearrange the ideal gas law equation as:
n = PV / RT
Step 2: Calculate the final number of moles of gas in the tire.
Using the same equation, but with the new temperature (T2), we can calculate the final number of moles (n2).
Step 3: Calculate the final pressure in the tire.
Using the ideal gas law equation, we can rearrange it to calculate the final pressure (P2) as:
P2 = n2RT2 / V
Step 4: Calculate the pressure rise in the tire.
The pressure rise can be calculated by subtracting the initial pressure (P1) from the final pressure (P2).
Pressure rise = P2 - P1
Calculation:
Given values:
T1 = 25°C = 298 K (Temperature in Kelvin)
P1 = 210 kPa (Initial pressure)
V = 0.025 m3 (Volume)
P0 = 100 kPa (Atmospheric pressure)
T2 = 50°C = 323 K (Final temperature)
Step 1:
Using the ideal gas law equation,
n = P1V / RT1
Step 2:
Using the ideal gas law equation,
n2 = P1V / RT2
Step 3:
Using the ideal gas law equation,
P2 = n2RT2 / V
Step 4:
Pressure rise = P2 - P1
Substituting the values:
Step 1:
n = (210 kPa)(0.025 m3) / (8.314 kPa·m3/K·mol)(298 K)
Step 2:
n2 = (210 kPa)(0.025 m3) / (8.314 kPa·m3/K·mol)(323 K)
Step 3:
P2 = (n2)(8.314 kPa·m3/K·mol)(323 K) / (0.025 m3)
Step 4:
Pressure rise = P2 - P1
Solution:
After solving the above equations, the pressure rise in the tire
Temperature of air in the tire (T1) = 25°C
Pressure reading on the gauge (P1) = 210 kPa
Volume of the tire (V) = 0.025 m3
Atmospheric pressure (P0) = 100 kPa
Temperature of air in the tire after rise (T2) = 50°C
Target:
To calculate the rise in pressure in the tire when the air temperature rises to 50°C.
Assumptions:
1. The tire is considered to be a closed system.
2. The ideal gas law is applicable.
3. The tire is assumed to be rigid and impermeable.
Explanation:
The ideal gas law equation is given by:
PV = nRT
Where,
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature
Step 1: Calculate the initial number of moles of gas in the tire.
To calculate the number of moles, we can rearrange the ideal gas law equation as:
n = PV / RT
Step 2: Calculate the final number of moles of gas in the tire.
Using the same equation, but with the new temperature (T2), we can calculate the final number of moles (n2).
Step 3: Calculate the final pressure in the tire.
Using the ideal gas law equation, we can rearrange it to calculate the final pressure (P2) as:
P2 = n2RT2 / V
Step 4: Calculate the pressure rise in the tire.
The pressure rise can be calculated by subtracting the initial pressure (P1) from the final pressure (P2).
Pressure rise = P2 - P1
Calculation:
Given values:
T1 = 25°C = 298 K (Temperature in Kelvin)
P1 = 210 kPa (Initial pressure)
V = 0.025 m3 (Volume)
P0 = 100 kPa (Atmospheric pressure)
T2 = 50°C = 323 K (Final temperature)
Step 1:
Using the ideal gas law equation,
n = P1V / RT1
Step 2:
Using the ideal gas law equation,
n2 = P1V / RT2
Step 3:
Using the ideal gas law equation,
P2 = n2RT2 / V
Step 4:
Pressure rise = P2 - P1
Substituting the values:
Step 1:
n = (210 kPa)(0.025 m3) / (8.314 kPa·m3/K·mol)(298 K)
Step 2:
n2 = (210 kPa)(0.025 m3) / (8.314 kPa·m3/K·mol)(323 K)
Step 3:
P2 = (n2)(8.314 kPa·m3/K·mol)(323 K) / (0.025 m3)
Step 4:
Pressure rise = P2 - P1
Solution:
After solving the above equations, the pressure rise in the tire
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The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer?
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The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer?.
The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer?.
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The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer?, a detailed solution for The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer? has been provided alongside types of The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. The volume of the tire is 0.025 m3 and the atmospheric pressure is 100 kPa.What will be the pressure rise (in kPa) in the tire when the air temperature in the tire rises to 50°C?(Rounded off to the nearest integer)Correct answer is '26'. Can you explain this answer? theory, EduRev gives you an
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