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Work done in isothermal and adiabatic compression
Concepts tested here
- adiabatic-vs-isothermal-compression-work
All Questions
2016 1 question
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A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then
The adiabatic curve is steeper, enclosing more area on compression.
Isothermal compression from V to $\frac{V}{2}$: $W = nRT\ln\left(\frac{V_f}{V_i}\right) = nRT\ln\left(\frac{1}{2}\right)$
Adiabatic compression: $W = \frac{k(V_f^{1-\gamma} - V_i^{1-\gamma})}{1 - \gamma}$, with $PV^\gamma$ = constant
The area under the adiabatic compression curve is greater than that under the isothermal compression curve.
Hence compressing the gas through the adiabatic process requires more work.