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 internal energy of the gas after adiabatic compression, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:
ΔU = Q - W
In this case, since the process is adiabatic (no heat exchange), there is no heat added or removed from the system. Therefore, the equation simplifies to:
ΔU = -W
So, to find the change in internal energy, we need to calculate the work done by the system. The work done during an adiabatic process can be calculated using the equation:
W = PΔV
Where P is the pressure applied on the gas, and ΔV is the change in volume.
Given:
Internal energy (before compression), U = 585 J
Change in volume, ΔV = -137 cm3 (since volume decreases)
Pressure applied, P = 2.65 atm
First, we need to convert the change in volume to SI units (m3) by dividing by 100000 (since 1 m3 = 100000 cm3):
ΔV = -137 cm3 ÷ 100000 = -0.00137 m3
Now we can calculate the work done:
W = PΔV
W = (2.65 atm) * (-0.00137 m3)
To proceed, we need to convert the pressure from atm to SI units (Pa) by multiplying by 101325 (since 1 atm = 101325 Pa):
P = 2.65 atm * 101325 Pa/atm = 267726.625 Pa
Now we can calculate the work done:
W = (267726.625 Pa) * (-0.00137 m3)
W ≈ -366.940 J
Since ΔU = -W, the change in internal energy is equal to the negative value of the work done:
ΔU = -( -366.940 J)
ΔU ≈ 366.940 J
Therefore, the internal energy of the gas after the adiabatic compression is approximately 366.940 J.