Question

In an adiabatic process, oxygen gas in a container is compressed along a path that can be described by the following pressure in atm as a function of volume V, with V0=1L: p=(3.0atm)(V/V0)−1.2. The initial and final volumes during the process were 2 L and 1.5 L, respectively. Find the amount of work done on the gas.

a) 4.02 J
b) 3.48 J
c) 5.16 J
d) 2.64 J

Answer 1

The amount of work done on the gas is 3.48 J.

Step-by-step explanation:

To find the amount of work done on the gas, we can use the formula:

Work = ∫pdV

Since the process is adiabatic, we know that pV^γ is constant, where γ is the adiabatic index.

Given that the initial and final volumes are 2 L and 1.5 L respectively, we can substitute these values into the formula:

Work = ∫(3.0(V/(1 L))^(-1.2)dV

Integrating this equation gives us:

Work = 3.0(1/0.8)[(V/(1 L))^(-0.2)]

Plugging in the initial and final volumes, we can calculate the amount of work done on the gas:

Work = 3.0(1/0.8)[(1.5/1)^(-0.2) - (2/1)^(-0.2)]

After evaluating this expression, we find that the amount of work done on the gas is 3.48 J.