Question

Work done by the gas in an isochoric process is _____. (where all the parameters V, T, P are standard)
1. W = 0
2. W = P (V2 – V1).
3. \(W=nRT\space ln(\frac{V_{final}}{V_{initial}})\)
4. \(W = \infty\)

Answer 1

Correct Answer - Option 1 : W = 0

CONCEPT:

• Work: The energy required to move a system or body or anything against a force is called work.

Different thermodynamic processes and their work done:

• Isobaric Process (Constant Pressure): Work done in an isobaric process is given by:

W = P ΔV

where W is Work done, P is the pressure and ΔV is change in volume.

• Isochoric Process (Constant Volume): Since volume is held constant i.e. ΔV = 0, Work done in an isochoric process is given by

W = P ΔV = 0

• For an isochoric process or constant volume process, work done is always zero.

• Isothermal Process (Constant Temperature): Work done in an isothermal process is given by,

\(W=nRT\space ln(\frac{V_{final}}{V_{initial}})\)

where W is Work done, n is the number of moles, R is the gas constant, T is temperature, and V is volume.

• Adiabatic Process (No Heat Transfer): An adiabatic system is perfectly insulated from the external environment and there is no heat transfer in or out of the system.

• Work done in an adiabatic process is due to a change in the internal energy of the system. 

\(W=P_{initial}V_{initial}^\gamma\space (\frac{V_{final}^{1-\gamma}-V_{initial}^{1-\gamma}}{1-\gamma})\)

​PVγ = C

where W is Work done, P is the pressure, V is volume, and γ is the adiabatic index or specific heat ratio of the gas.

EXPLANATION:

• Isochoric Process (Constant Volume): Since volume is held constant i.e. ΔV = 0, 

Work done in an isochoric process is given by:

W = P ΔV = 0

• For an isochoric process or constant volume process, work done is always zero.
• So the correct answer is option 1.