The internal energy of a gas is 585 J. The gas is compressed adiabatically, and its volume decreases by 137 cm3. If the pressure applied on the gas during compression is 2.65 atm, what is the internal energy of the gas after the adiabatic compression?
To find the final internal energy of the gas after adiabatic compression, we need to consider the first law of thermodynamics, which states that the change in internal energy of a system is equal to the work done on the system plus the heat added to the system.
In this case, since the compression is adiabatic, which means no heat is exchanged with the surroundings, the equation simplifies to:
ΔU = W
where:
- ΔU is the change in internal energy
- W is the work done on the system
To find the work done on the gas, we can use the formula:
W = PΔV
where:
- P is the pressure applied on the gas
- ΔV is the change in volume
Given:
- ΔV = 137 cm³ = 0.137 L (since 1 cm³ = 0.001 L)
- P = 2.65 atm
Substituting the values into the formula, we get:
W = (2.65 atm) * (0.137 L)
W = 0.36305 atm L
But the unit of work is Joules (J), so we need to convert atm L to J.
Since 1 atm L = 101.325 J, we can multiply by this conversion factor:
W = (0.36305 atm L) * (101.325 J / 1 atm L)
W ≈ 36.78 J
Finally, substituting the value of work (W) into the equation ΔU = W, we get:
ΔU = 36.78 J
Therefore, the internal energy of the gas after adiabatic compression is approximately 36.78 J.