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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.
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
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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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