The work done by a gas when its 0.5 mole at 27°C expands from 5 lit to 25 lit reversibly and isothermally is -x kJ. Find value of x ?
Question
The work done by a gas when its 0.5 mole at 27°C expands from 5 lit to 25 lit reversibly and isothermally is -x kJ. Find value of x ?
Solution
To find the value of x, we can use the formula for the work done by a gas during an isothermal expansion:
Work = -nRT ln(V2/V1)
Where:
- n is the number of moles of the gas (0.5 mol in this case)
- R is the ideal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin (27°C = 300 K)
- V1 is the initial volume (5 L)
- V2 is the final volume (25 L)
Plugging in the values, we have:
Work = -(0.5 mol)(8.314 J/mol·K)(300 K) ln(25 L/5 L)
Simplifying further:
Work = -1247.1 J ln(5)
Using the natural logarithm of 5:
Work ≈ -1247.1 J (1.609)
Calculating the value:
Work ≈ -2004.4 J
Since the question asks for the value of x in kJ, we convert the result to kJ:
x = 2004.4 J / 1000 = 2.0044 kJ
Therefore, the value of x is approximately 2.0044 kJ.
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