Question

two samples of gas is initially at same temp,pressure and volume. one sample is compressed from v to v/2 isothermally and other one is compressed from v to v/2 adiabatically then increase in pressure is more in adiabatic than in isothermal comp why???

Answer 1

Answer on Question #41156, Physics, Molecular Physics

Question: two samples of gas is initially at same temp, pressure and volume. one sample is compressed from v to v/2 isothermally and other one is compressed from v to v/2 adiabatically then increase in pressure is more in adiabatic than in isothermal comp why?

Solution. Thats because the isotermic change of pressure is inverse proportion to change of volume

$PV=const,\qquad P\sim\frac{1}{V}$

while adiabatic one is

$PV^{\gamma}=const,\qquad P\sim\frac{1}{V^{\gamma}}$

where $\gamma$ is adiabatic costant and is bigger then 1. Hence, with the same change of volume the pressure decrease more rapid in adiabatic process.

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