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The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3?
Most Upvoted Answer
The work done on the system when one mole of an ideal gas is compresse...
Given:
- One mole of an ideal gas
- Isothermal compression
- Final volume = 0.01 m^3
- External pressure = 5 bar
- Work done on the system = 20 kJ
To find: Initial volume of the gas
Formula:
For isothermal process, work done on the system is given by:
W = nRTln(V2/V1)
where,
W = work done on the system
n = number of moles of gas
R = gas constant
T = temperature
V1 = initial volume
V2 = final volume
Approach:
1. Calculate the value of R using the ideal gas equation: PV = nRT, where P = 5 bar, V = 0.01 m^3, n = 1 mole and T = constant (since isothermal process)
2. Substitute the values of n, R, T, V2 and W in the formula for work done and solve for V1
3. Round off the answer to two decimal places
Solution:
1. Calculation of gas constant R:
PV = nRT
5 * 10^5 Pa * 0.01 m^3 = 1 mol * R * T
R = 5 * 10^4 J/mol.K
2. Calculation of initial volume V1:
W = nRTln(V2/V1)
20 * 10^3 J = 1 mol * 5 * 10^4 J/mol.K * T * ln(V2/V1)
ln(V2/V1) = 0.4
V2/V1 = e^0.4
V1 = V2/e^0.4
V1 = 0.045 m^3
Answer: The initial volume of the gas is 0.045 m^3.
Therefore, option A-0.045m^3 is the correct answer.
- One mole of an ideal gas
- Isothermal compression
- Final volume = 0.01 m^3
- External pressure = 5 bar
- Work done on the system = 20 kJ
To find: Initial volume of the gas
Formula:
For isothermal process, work done on the system is given by:
W = nRTln(V2/V1)
where,
W = work done on the system
n = number of moles of gas
R = gas constant
T = temperature
V1 = initial volume
V2 = final volume
Approach:
1. Calculate the value of R using the ideal gas equation: PV = nRT, where P = 5 bar, V = 0.01 m^3, n = 1 mole and T = constant (since isothermal process)
2. Substitute the values of n, R, T, V2 and W in the formula for work done and solve for V1
3. Round off the answer to two decimal places
Solution:
1. Calculation of gas constant R:
PV = nRT
5 * 10^5 Pa * 0.01 m^3 = 1 mol * R * T
R = 5 * 10^4 J/mol.K
2. Calculation of initial volume V1:
W = nRTln(V2/V1)
20 * 10^3 J = 1 mol * 5 * 10^4 J/mol.K * T * ln(V2/V1)
ln(V2/V1) = 0.4
V2/V1 = e^0.4
V1 = V2/e^0.4
V1 = 0.045 m^3
Answer: The initial volume of the gas is 0.045 m^3.
Therefore, option A-0.045m^3 is the correct answer.
Community Answer
The work done on the system when one mole of an ideal gas is compresse...
D
w=-P (v2-v1)
-20*10^3 /5*10^5)+. 01
. 05
w=-P (v2-v1)
-20*10^3 /5*10^5)+. 01
. 05
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The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3?
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The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3?.
The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The work done on the system when one mole of an ideal gas is compressed isothermally to a final volume of 0.01 m^3 at constand external pressure of 5 bar is 20kJ. What is the initial volume of the gas? A-0.045m^3 B-0.035m^3 C-0.025m^3 D-0.05m^3 E-0.04m^3?.
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