The air within a piston equipped with a cylinder absorbs 570J of heat and expands from an initial volume of 0.12L to a final volume of 0.88L against an external pressure of 1.0 atm. What is the change in internal energy of the air within the piston?
delta E = w + q
q=570 J
V1 = 0.12 L
V2 = 0.88 L
delta V = 0.88 L - 0.12 L = 0.76 L
w = -P x delta V
w = -1.0 atm x 0.76 L = -0.76 L atm
You need to convert L atm to J
-0.76 L atm / 1 L atm x 101.3 J = -76.99 J
delta E = -76.99 J + 570 J = 493 J
Mastering Chemistry accepts this answer as Correct
Well, here's a question that really takes the air out of the room! But fear not, my inquisitive friend, for the clown is here to bring some energy (pun intended) to the party!
To determine the change in internal energy of the air within the piston, 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.
In this case, the air within the piston absorbs 570J of heat. So, we can say that the heat added to the system is 570J.
Now, let's calculate the work done by the system. Since the air expands against an external pressure of 1.0 atm, we can use the equation:
Work = Pressure * Change in Volume
The change in volume is given by the difference between the final volume (0.88L) and the initial volume (0.12L), which is equal to 0.88L - 0.12L = 0.76L.
Converting the volume from liters to cubic meters (SI units) gives us 0.76L * 0.001m^3/L = 0.00076m^3.
Now, we can calculate the work done:
Work = 1.0 atm * 0.00076m^3 = 0.00076 J
Finally, we can determine the change in internal energy:
Change in Internal Energy = Heat added - Work done
Change in Internal Energy = 570J - 0.00076J = 569.99924J
So, the change in internal energy of the air within the piston is approximately 569.99924J.
And there you have it! I hope my clown calculations didn't blow hot air your way!
To find the change in internal energy of the air within the piston, we can use the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system.
The change in internal energy (ΔU) is given by the equation:
ΔU = Q - W
Where:
ΔU = Change in internal energy
Q = Heat added to the system
W = Work done by the system
In this case, the heat added to the system is given as 570 J. To calculate the work done by the system, we need to determine the pressure-volume work (W_pv).
The pressure-volume work is given by the equation:
W_pv = PΔV
Where:
W_pv = Pressure-volume work
P = Pressure
ΔV = Change in volume
In this case, the external pressure (P) is given as 1.0 atm, and the change in volume (ΔV) is given as 0.88 L - 0.12 L = 0.76 L.
To calculate the work done by the system, we need to convert the volume from liters to cubic meters, since the pressure is given in atmospheres.
1 L = 0.001 m^3
Therefore, the change in volume (ΔV) is equal to 0.76 L * 0.001 m^3/L = 0.00076 m^3.
Now we can substitute the values into the equation to find the pressure-volume work:
W_pv = PΔV = (1.0 atm) * (0.00076 m^3) = 0.00076 atm∙m^3
Finally, we can calculate the change in internal energy by substituting the values into the equation:
ΔU = Q - W = 570 J - 0.00076 atm∙m^3
Therefore, the change in internal energy of the air within the piston is 569.99924 J (rounded to four decimal places).
To find the change in internal energy of the air within the piston, we can use the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added (Q) minus the work done by the system (W).
The formula is: ΔU = Q - W
Given:
Heat added (Q) = 570 J
Initial volume (V1) = 0.12 L
Final volume (V2) = 0.88 L
External pressure (P) = 1.0 atm
First, let's find the work done by the system (W). The work done is given by the equation:
W = -PΔV
Where ΔV is the change in volume, which is equal to V2 - V1.
ΔV = V2 - V1 = 0.88 L - 0.12 L = 0.76 L
Now we can calculate the work done:
W = -PΔV = -(1.0 atm) * (0.76 L) = -0.76 atm·L
Next, we can substitute the given values for heat added (Q) and work done (W) into the formula for the change in internal energy:
ΔU = Q - W
ΔU = 570 J - (-0.76 atm·L)
However, we need to convert the work done from atm·L to joules, since the units need to be consistent. To convert atm·L to joules, we use the conversion factor:
1 atm·L = 101.325 J
W = -0.76 atm·L * 101.325 J/atm·L ≈ -76.99 J
Substituting this value into the equation for ΔU:
ΔU = 570 J - (-76.99 J)
ΔU = 646.99 J
Therefore, the change in internal energy of the air within the piston is approximately 646.99 J.