Question

one litre of nitrogen at 15 degree celsius and 10^6 Pa expands isothermally until its volume is doubled and then adiabatically until it is redoubled.find the final pressure of gas.

Answer 1

Answer on Question #45070, Physics, Molecular Physics — Thermodynamics

one litre of nitrogen at 15 degree celsius and $10^{6}$ Pa expands isothermally until its volume is doubled and then adiabatically until it is redoubled.find the final pressure of gas.

Solution

Pressure after the isothermal expansion

$p_{0}V_{0}=p_{1}V_{1}$

$p_{1}=\frac{V_{0}}{V_{1}}p_{0}=\frac{1}{2}p_{0}$

Pressure after adiabatic expansion

$p_{2}V_{2}^{\gamma}=p_{1}V_{1}^{\gamma}$

$p_{2}=p_{1}\frac{V_{1}^{\gamma}}{V_{2}^{\gamma}},\qquad\gamma=7/3$

$p_{2}=p_{1}\frac{1}{2^{7/3}}=p_{0}\cdot\frac{1}{2}\cdot\frac{1}{2^{7/3}}\approx 0.1p_{0}=10^{5}\,Pa$

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