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A cylinder contains 5m3 of ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is
- a)804.7
- b)953.2
- c)981.7
- d)1012.2
Correct answer is option 'A'. Can you explain this answer?
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A cylinder contains 5m3 of ideal gas at a pressure of 1 bar. This gas ...
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A cylinder contains 5m3 of ideal gas at a pressure of 1 bar. This gas ...
Given:
- Initial volume of the cylinder = 5 m^3
- Initial pressure of the gas = 1 bar
- Final pressure of the gas = 5 bar
To find:
The work in kJ required for this process.
Assumptions:
- The gas is ideal, which means it obeys the ideal gas law.
- The process is reversible, which means it can be reversed without any loss or gain of energy.
- The process is isothermal, which means the temperature of the gas remains constant throughout the process.
Formula:
The work done in an isothermal process can be calculated using the formula:
W = nRT ln(V2/V1)
Where:
- W = work done
- n = number of moles of gas
- R = ideal gas constant (8.314 J/mol·K)
- T = temperature (in Kelvin)
- V1 = initial volume
- V2 = final volume
Calculation:
Given that the initial volume (V1) is 5 m^3 and the initial pressure (P1) is 1 bar, we can use the ideal gas law to find the number of moles (n) of gas.
PV = nRT
n = PV / RT
Substituting the given values:
n = (1 bar * 5 m^3) / (8.314 J/mol·K * 273 K)
n ≈ 0.000237 mol
Since the process is isothermal, the temperature remains constant throughout the process. Therefore, we can use the same temperature value for both V1 and V2.
Now, we can calculate the work done using the formula:
W = nRT ln(V2/V1)
W = (0.000237 mol * 8.314 J/mol·K * 273 K) ln(5 m^3 / 5 m^3)
W ≈ 804.7 J
Converting the work done from Joules to kilojoules:
W ≈ 0.8047 kJ
Therefore, the work required for the process is approximately 0.8047 kJ, which is closest to option 'A' (804.7 kJ).
- Initial volume of the cylinder = 5 m^3
- Initial pressure of the gas = 1 bar
- Final pressure of the gas = 5 bar
To find:
The work in kJ required for this process.
Assumptions:
- The gas is ideal, which means it obeys the ideal gas law.
- The process is reversible, which means it can be reversed without any loss or gain of energy.
- The process is isothermal, which means the temperature of the gas remains constant throughout the process.
Formula:
The work done in an isothermal process can be calculated using the formula:
W = nRT ln(V2/V1)
Where:
- W = work done
- n = number of moles of gas
- R = ideal gas constant (8.314 J/mol·K)
- T = temperature (in Kelvin)
- V1 = initial volume
- V2 = final volume
Calculation:
Given that the initial volume (V1) is 5 m^3 and the initial pressure (P1) is 1 bar, we can use the ideal gas law to find the number of moles (n) of gas.
PV = nRT
n = PV / RT
Substituting the given values:
n = (1 bar * 5 m^3) / (8.314 J/mol·K * 273 K)
n ≈ 0.000237 mol
Since the process is isothermal, the temperature remains constant throughout the process. Therefore, we can use the same temperature value for both V1 and V2.
Now, we can calculate the work done using the formula:
W = nRT ln(V2/V1)
W = (0.000237 mol * 8.314 J/mol·K * 273 K) ln(5 m^3 / 5 m^3)
W ≈ 804.7 J
Converting the work done from Joules to kilojoules:
W ≈ 0.8047 kJ
Therefore, the work required for the process is approximately 0.8047 kJ, which is closest to option 'A' (804.7 kJ).
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A cylinder contains 5m3 of ideal gas at a pressure of 1 bar. This gas iscompressed in a reversible isothermal process till its pressure increases to 5 bar.The work in kJ required for this process isa)804.7b)953.2c)981.7d)1012.2Correct answer is option 'A'. Can you explain this answer?
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