Question

an ideal monatomic gas expands adiabatically from a state with pressure 8.1x10^5 Pa and volume 2.5x10^-3 m^3 to a state of volume 4.6x10^-3 m^3, calculate the new pressure of the gas

Answer 1

For monoatomic gas $γ=\frac{C_p}{C_v}=\frac{(5/2)R}{(3/2)R}=\frac{5}{3}$

The equation for adiabatic expansion is $PV^γ=constant$

Find constant C:

$C=P_1V_1^γ = (8.1 \times 10^5Pa)(2.5 \times 10^{-3}m^3)^{\frac{5}{3}}$

The constant c is fixed for the entire process and can be used to find P_2

$C=P_2V_2^γ = P_2(4.6\times10^{-3}m^3)^\frac{5}{3}$

$P_1V_1^γ=P_2V_2^γ$

$(8.1\times10^5 Pa)(2.5\times10^{-3}m^3)\frac{5}{3}=P_2(4.6\times10^{-3}m^3)\frac{5}{3}$

$\frac{8.1\times10^5}{P_2}=(\frac{4.6\times10^{-3}}{2.5\times10^{-3}})^\frac{5}{3}$

$P_2 = 2.9\times10^5 Pa$