Question:
An ideal gas expands from volume $V_{1}$ to $V_{2}$ through an isothermal reversible process. The work done by the system is given by
An ideal gas expands from volume $V_{1}$ to $V_{2}$ through an isothermal reversible process. The work done by the system is given by
Show Hint
In standard IUPAC convention, expansion work is negative because energy leaves the system, giving us the signature negative sign: $-nRT \ln(V_{2}/V_{1})$.
Updated On: Jun 3, 2026
- $W = -nRT \ln\left(\frac{V_{2}}{V_{1}}\right)$
- $W = nRT \ln\left(\frac{V_{2}}{V_{1}}\right)$
- $W = zero$
- $W = -P\Delta V$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept
In thermodynamics, the work done during a reversible transformation is calculated by integrating the expression $W = -\int P \, dV$.
Step 2: Meaning
For an ideal gas equation, we substitute $P = \frac{nRT}{V}$ into the integral since the process is isothermal ($T$ remains constant).
Step 3: Analysis
Performing the definite integration from the initial volume $V_{1}$ to the final volume $V_{2}$: $$W = -\int_{V_{1}}^{V_{2}} \frac{nRT}{V} \, dV = -nRT \int_{V_{1}}^{V_{2}} \frac{1}{V} \, dV$$ $$W = -nRT [\ln V]_{V_{1}}^{V_{2}} = -nRT \ln\left(\frac{V_{2}}{V_{1}}\right)$$
Step 4: Conclusion
This matches the standard thermodynamic representation for reversible isothermal work done by an expanding system.
Final Answer: (A)
In thermodynamics, the work done during a reversible transformation is calculated by integrating the expression $W = -\int P \, dV$.
Step 2: Meaning
For an ideal gas equation, we substitute $P = \frac{nRT}{V}$ into the integral since the process is isothermal ($T$ remains constant).
Step 3: Analysis
Performing the definite integration from the initial volume $V_{1}$ to the final volume $V_{2}$: $$W = -\int_{V_{1}}^{V_{2}} \frac{nRT}{V} \, dV = -nRT \int_{V_{1}}^{V_{2}} \frac{1}{V} \, dV$$ $$W = -nRT [\ln V]_{V_{1}}^{V_{2}} = -nRT \ln\left(\frac{V_{2}}{V_{1}}\right)$$
Step 4: Conclusion
This matches the standard thermodynamic representation for reversible isothermal work done by an expanding system.
Final Answer: (A)
Was this answer helpful?
0
0
Top AP EAPCET Chemistry Questions
- The four quantum numbers of the valence electron of potassium are :
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
- In which of the following the election gain enthalpy of elements is correctly arranged?
- The radii of $ \text{F,}{{\text{F}}^{-}}\text{O} $ and $ {{\text{O}}^{2-}} $ are in the order
- Which of the following has the highest first ionization potential?
View More Questions
Top AP EAPCET Thermodynamics Questions
- For one mole of an ideal gas, three isochors were obtained at \(V_1, V_2\) and \(V_3\) respectively. Their slopes are \(m_1, m_2\) and \(m_3\). If \(V_1<V_2<V_3\), then the correct relationship of slopes is:
- The enthalpy change (ΔH) for the reaction N2(g) + 3H2(g) → 2NH3(g) is -92 kJ/mol.
What is the enthalpy change for the decomposition of 1 mol of NH3(g) into its elements? - Identify the correct statements from the following. (i). For adiabatic process, $\Delta U = W_{adiabatic$} (ii). Work is a path function. (iii). Volume is an extensive property.
- Hydration enthalpy of which of the following ions is highest?
- The standard Gibbs energy ($\Delta G^\ominus$) for the following reaction is A(s) + B$^{2+}$ (aq) $\rightleftharpoons$ A$^{2+}$ (aq) + B(s), K$_c$=10$^{12}$ at 25$^\circ$C (K$_c$= equilibrium constant)
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions