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A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes
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A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is firs...
When an ideal gas is heated at constant volume, its temperature increases but its pressure remains the same. Therefore, the final pressure of the gas after it is heated to 131 degrees Celsius is still 9 atm.
When the amount of an ideal gas is increased at constant volume and temperature, its pressure increases. However, the final pressure of the gas depends on the amount of the increase and the original pressure.
If the amount of the gas is increased by 50%, then the final amount of the gas is 1.5 times the original amount. Therefore, the final pressure of the gas is 1.5 times the original pressure, which is 9 atm * 1.5 = 13.5 atm.
Therefore, the final pressure of the gas after it is heated and the amount is increased by 50% is 13.5 atm.
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A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is firs...
Initial Conditions
- The gas is at an initial pressure of 9 atm.
- The initial temperature is 30°C, which converts to Kelvin as follows:
- T1 = 30 + 273.15 = 303.15 K.
Heating at Constant Volume
- The gas is heated to 131°C.
- The temperature in Kelvin is:
- T2 = 131 + 273.15 = 404.15 K.
- Since the volume is constant, we can use the ideal gas law in the form of \( P_1/T_1 = P_2/T_2 \) to find the new pressure \( P_2 \).
Calculating New Pressure
- Rearranging the formula gives:
- \( P_2 = P_1 \times (T_2/T_1) \).
- Substituting the values:
- \( P_2 = 9 \, \text{atm} \times (404.15 \, \text{K} / 303.15 \, \text{K}) \).
- \( P_2 \approx 9 \times 1.333 = 12 \, \text{atm} \).
Increasing the Amount of Gas
- The amount of gas is increased by 50% at constant volume and temperature.
- This means the new number of moles \( n_2 = 1.5n_1 \).
Final Pressure Calculation
- Using the ideal gas law \( PV = nRT \) at constant volume and temperature, the final pressure \( P_3 \) can be expressed as:
- \( P_3 = (n_2/n_1) \times P_2 \).
- Plugging in values:
- \( P_3 = 1.5 \times 12 \, \text{atm} = 18 \, \text{atm} \).
Conclusion
- The final pressure of the gas after heating and increasing the amount by 50% is 18 atm.
- The gas is at an initial pressure of 9 atm.
- The initial temperature is 30°C, which converts to Kelvin as follows:
- T1 = 30 + 273.15 = 303.15 K.
Heating at Constant Volume
- The gas is heated to 131°C.
- The temperature in Kelvin is:
- T2 = 131 + 273.15 = 404.15 K.
- Since the volume is constant, we can use the ideal gas law in the form of \( P_1/T_1 = P_2/T_2 \) to find the new pressure \( P_2 \).
Calculating New Pressure
- Rearranging the formula gives:
- \( P_2 = P_1 \times (T_2/T_1) \).
- Substituting the values:
- \( P_2 = 9 \, \text{atm} \times (404.15 \, \text{K} / 303.15 \, \text{K}) \).
- \( P_2 \approx 9 \times 1.333 = 12 \, \text{atm} \).
Increasing the Amount of Gas
- The amount of gas is increased by 50% at constant volume and temperature.
- This means the new number of moles \( n_2 = 1.5n_1 \).
Final Pressure Calculation
- Using the ideal gas law \( PV = nRT \) at constant volume and temperature, the final pressure \( P_3 \) can be expressed as:
- \( P_3 = (n_2/n_1) \times P_2 \).
- Plugging in values:
- \( P_3 = 1.5 \times 12 \, \text{atm} = 18 \, \text{atm} \).
Conclusion
- The final pressure of the gas after heating and increasing the amount by 50% is 18 atm.
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A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes
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A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes.
A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain mass of an ideal gas at 9 atm and 30 degrees Celsius is first heated to 131 degrees Celsius at constant volume and then the amount of the gas is increased by 50% at constant volume and temperature.The final pressure of the gas becomes.
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