A gas in a cylinder with a piston that slides freely within is adiabatically expanded from 1.5 to 1.7 m³.If the pressure exerted by the walls on its container during the expansion was 2.0atm,by what amount did the internal energy of the gas change during this expansion?

Question

Quizplus · Accepted Answer

Since the expansion is adiabatic, there is no heat transferred between the gas and the environment. Therefore, the change in internal energy is equal to the work done on the gas: 
ΔU = -W 
where W is the work done on the gas. 
The work done on the gas can be calculated using: 
W = PΔV 
where P is the pressure and ΔV is the change in volume. 
ΔV = V2 -V1 = (1.7 m^3 - 1.5 m^3) = 0.2 m^3. 
Thus, 
W = (2.0 atm)(0.2 m^3) = 0.4 L⋅atm = 40 J 
Since the volume increased, the internal energy of the gas decreased: 
ΔU = -W = -40 J = -40 kJ 
Therefore, the correct answer is B: -41 kJ.

A Gas in a Cylinder with a Piston That Slides