Work Done In Expansion
One mole of an ideal gas expands isothermally and reversibly at 300 K from a volume of 10 L to 50 L. What is the work done by the gas? (R = 8.314 J/mol·K)
Select the correct option:
Solution
-4014 J
For a reversible isothermal expansion of an ideal gas, the work done by the gas is given by (w = -nRT\ln(V_f/V_i)). This formula arises from integrating (p,dV) along a reversible path where (p = nRT/V). Here (n = 1) mol, (R = 8.314) J/mol·K, (T = 300) K, (V_i = 10) L, (V_f = 50) L. (w = -(1)(8.314)(300)\ln(50/10) = -2494.2 \times \ln(5) = -2494.2 \times 1.6094 = -4014) J. The negative sign indicates the gas does work on the surroundings (energy leaves the system as work). Option -3988 J results from using (\log_{10}) instead of natural logarithm without the necessary conversion factor. Option +4014 J has the wrong sign — work done BY the gas in expansion should be negative for the system. Option -2490 J omits the logarithm and uses a simple ratio incorrectly. This is a standard NCERT reversible work calculation. Plausibility check: for expansion from 10 L to 50 L at moderate temperature, a work magnitude near 4 kJ is physically reasonable for one mole of ideal gas.
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About This Question
- Subject
- chemistry
- Chapter
- chemical thermodynamics
- Topic
- work done in expansion
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
-4014 J
For a reversible isothermal expansion of an ideal gas, the work done by the gas is given by (w = -nRT\ln(V_f/V_i)). This formula arises from integrating (p,dV) along a reversible path where (p = nRT/V). Here (n = 1) mol, (R = 8.314) J/mol·K, (T = 300) K, (V_i = 10) L, (V_f = 50) L. (w = -(1)(8.314)(300)\ln(50/10) = -2494.2 \times \ln(5) = -2494.2 \times 1.6094 = -4014) J. The negative sign indicates the gas does work on the surroundings (energy leaves the system as work). Option -3988 J results from using (\log_{10}) instead of natural logarithm without the necessary conversion factor. Option +4014 J has the wrong sign — work done BY the gas in expansion should be negative for the system. Option -2490 J omits the logarithm and uses a simple ratio incorrectly. This is a standard NCERT reversible work calculation. Plausibility check: for expansion from 10 L to 50 L at moderate temperature, a work magnitude near 4 kJ is physically reasonable for one mole of ideal gas.
This medium difficulty chemistry question is from the chapter chemical thermodynamics, covering the topic of work done in expansion. It appeared in the 2025 exam.
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