Question

An insulated piston cylinder device contains 5 liters of an ideal gas at a pressure of 2 bar. The gas is compressed adiabatically to a final volume of 2 liters. If the initial temperature of the gas is 300 K, what is the final temperature of the gas?

Answer 1

To find the final temperature of the gas, use the adiabatic equation.

Step-by-step explanation:

To find the final temperature of the gas, we can use the adiabatic equation:

T₂ = T₁ * (V₁/V₂)^[(y-1)/y]

Where T₂ is the final temperature, T₁ is the initial temperature (300 K), V₁ is the initial volume (5 L), V₂ is the final volume (2 L), and y is the heat capacity ratio for the gas (given as y = 7/5 for ideal diatomic gases).

Plugging in the values, we get:

T₂ = 300 * (5/2)^[(7/5-1)/(7/5)]

Simplifying the equation, we find that the final temperature of the gas is approximately 578 K.