A gas is compressed from an initial volume of 5.60 L to a final volume of 1.22 L by an external pressure of 1.00 atm. During the compression the gas releases 128 J of heat.
What is the change in internal energy of the gas?
To find the change in internal energy of the gas, we can use the first law of thermodynamics, which states that the change in internal energy is equal to the sum of heat added to the system and the work done by or on the system:
ΔU = Q + W
Where:
ΔU is the change in internal energy
Q is the heat added to the system
W is the work done by or on the system
In this case, we are given that the gas releases 128 J of heat (Q = -128 J). We need to determine the work done on the system (W) in order to find the change in internal energy (ΔU).
The work done on the system can be calculated using the formula:
W = -PΔV
Where:
P is the external pressure
ΔV is the change in volume
In this case, the external pressure is given as 1.00 atm and the change in volume is from an initial volume of 5.60 L to a final volume of 1.22 L. Therefore:
ΔV = 1.22 L - 5.60 L = -4.38 L
Note that the negative sign indicates that the work is done on the system rather than by the system.
Now we can substitute the values into the formula to calculate the work:
W = -PΔV = -(1.00 atm)(-4.38 L) = 4.38 atm·L
Finally, we can substitute the values of Q and W into the first law of thermodynamics equation to find the change in internal energy:
ΔU = Q + W = -128 J + 4.38 atm·L
Since the units for Q (Joules) and W (atm·Liters) are different, we need to convert the units so they are consistent. We can convert atm·L to Joules using the conversion factor 1 atm·L = 101.325 J. Therefore:
ΔU = -128 J + (4.38 atm·L)(101.325 J/atm·L)
Calculating this expression will give you the change in internal energy of the gas.