A monatomic ideal gas is compressed adiabatically from a pressure of 1.39 105 Pa and volume of 260 L to a volume of 39.0 L. What is the new pressure of the gas?

In an adiabatic compression,

P*V^gamma = constant

where "gamma" is the specific heat ratio, Cp/Cv, which is 5/3 for a monatomic gas.
Therefore,
P2/P1 = [V1/V2)^5/3 = (260/39)^5/3
= 23.62

P2 = 3.28*10^6 Pa

Thank you very much

To find the new pressure of the gas after adiabatic compression, we can use the adiabatic compression equation:

P1 * V1^γ = P2 * V2^γ

Where:
P1 = initial pressure of the gas (1.39 * 10^5 Pa)
V1 = initial volume of the gas (260 L)
P2 = final pressure of the gas (to be determined)
V2 = final volume of the gas (39.0 L)
γ = heat capacity ratio for a monatomic ideal gas (5/3)

Now let's solve for P2:

P1 * V1^γ = P2 * V2^γ

(1.39 * 10^5 Pa) * (260 L)^5/3 = P2 * (39.0 L)^5/3

Simplifying the equation:
(1.39 * 10^5 Pa) = P2 * ((39.0 L) / (260 L))^5/3

(1.39 * 10^5 Pa) = P2 * (0.15)^5/3

(1.39 * 10^5 Pa) = P2 * 0.0610638

Solving for P2:
P2 = (1.39 * 10^5 Pa) / 0.0610638 = 2.27788 * 10^6 Pa

Therefore, the new pressure of the gas after adiabatic compression is approximately 2.28 * 10^6 Pa.