calculate the internal energy change for each of the following.

a. one hundred(100.)joules of work are required to compress a gas. at the same time the gas releases 23 J of heat.
b. a piston is compressed from a volume of 8.30 L to 2.80 L against a constant pressure of 1.90 atm. in the process, there is a heat gain by the system of 350. J.
c. a piston expands against 1.00 atm of pressure from 11.2 L to 29.1 L. in the process, 1037 J of heat is absorbed.

delta E = delta H + w and w = -P*delta V.

Watch the signs.

a. To calculate the internal energy change, we need to use the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W).

ΔU = Q - W

Given that the gas releases 23 J of heat (Q = -23 J) and 100 J of work is required to compress it (W = 100 J), we can calculate the internal energy change as follows:

ΔU = -23 J - 100 J
ΔU = -123 J

Therefore, the internal energy change for this process is -123 J.

b. In this case, the process occurs against a constant pressure of 1.90 atm. The work done on the system can be calculated using the formula:

W = -PΔV

where P is the pressure and ΔV is the change in volume.

Given that the pressure is constant at 1.90 atm, the change in volume is ΔV = 8.30 L - 2.80 L = 5.50 L.

W = -1.90 atm * 5.50 L
W = -10.45 atm * L

Now, to calculate the internal energy change, we can use the first law of thermodynamics:

ΔU = Q - W

Given that there is a heat gain by the system of 350 J (Q = 350 J), we have:

ΔU = 350 J - (-10.45 atm * L)
ΔU = 350 J + 10.45 atm * L

Therefore, the internal energy change for this process is 350 J + 10.45 atm * L.

c. The work done by the system can be calculated using the same formula as in part b:

W = -PΔV

Given a pressure of 1.00 atm and a change in volume of ΔV = 29.1 L - 11.2 L = 17.9 L, we have:

W = -1.00 atm * 17.9 L
W = -17.9 atm * L

Using the first law of thermodynamics, we can calculate the internal energy change:

ΔU = Q - W

Given that 1037 J of heat is absorbed by the system (Q = 1037 J), we have:

ΔU = 1037 J - (-17.9 atm * L)
ΔU = 1037 J + 17.9 atm * L

Therefore, the internal energy change for this process is 1037 J + 17.9 atm * L.

To calculate the internal energy change for each situation, we need to use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to or removed from the system minus the work (W) done by or on the system.

a. In this case, the work done on the system is 100 J (negative sign since work is done on the gas), and the heat released by the system is 23 J. Therefore, the internal energy change (ΔU) can be calculated as follows:
ΔU = Q - W
ΔU = 23 J - (-100 J)
ΔU = 23 J + 100 J
ΔU = 123 J

So, the internal energy change is 123 Joules.

b. In this case, we need to calculate the work done on the system and the heat gain by the system.
The work done on the system can be calculated using the formula:
W = PΔV
W = 1.90 atm * (2.80 L - 8.30 L)

Since the volume is decreasing, the work done is negative (work is done on the system). Now we can calculate the work:
W = -1.9 atm * (8.3 L - 2.8 L)
W = -1.9 atm * 5.5 L
W = -10.45 atm·L

In this case, the heat gain by the system is given as 350 J. Therefore, the internal energy change (ΔU) can be calculated as follows:
ΔU = Q - W
ΔU = 350 J - (-10.45 atm·L)
ΔU = 350 J + 10.45 atm·L

Note that atm·L is a unit of work. To convert it to joules (J), we can use the conversion factor 1 atm·L = 101.3 J. Therefore:
ΔU = 350 J + (10.45 atm·L * 101.3 J/atm·L)
ΔU = 350 J + 1057.285 J
ΔU = 1407.285 J

So, the internal energy change is 1407.285 Joules.

c. In this case, the system is absorbing 1037 J of heat. Since the volume is increasing, the work done by the system is positive. The work done by the system can be calculated using the same formula as in case b:
W = PΔV
W = 1.00 atm * (29.1 L - 11.2 L)
W = 1.00 atm * 17.9 L
W = 17.9 atm·L

Therefore, the internal energy change (ΔU) can be calculated as follows:
ΔU = Q - W
ΔU = 1037 J - (17.9 atm·L * 101.3 J/atm·L)
ΔU = 1037 J - 1813.270 J
ΔU = -776.270 J

So, the internal energy change is -776.270 Joules (negative indicates a decrease in internal energy).