The air within a piston equipped with a cylinder absorbs 555 J of heat and expands from an initial volume of 0.12 L to a final volume of 0.87 L against an external pressure of 1.0 atm.
What is the change in internal energy of the air within the piston in Joules?
delta E = q + w
w = -p*delta v = -p*(V2-V1)
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The change in internal energy of the air can be calculated using 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 work done by the system can be calculated using the formula:
Work = -P * ΔV
where P is the external pressure and ΔV is the change in volume.
Given that the external pressure (P) is 1.0 atm and the change in volume (ΔV) is 0.87 L - 0.12 L = 0.75 L, we can calculate the work done by the system:
Work = -1.0 atm * 0.75 L = -0.75 atm L
Now, let's calculate the change in internal energy:
Change in internal energy = Heat - Work
= 555 J - (-0.75 atm L)
Since the units of heat and work are different (Joules and atm L, respectively), we need to convert the units before subtracting:
1 atm L = 101.325 J
Change in internal energy = 555 J - (-0.75 atm L * 101.325 J/atm L)
= 555 J + 75.99375 J
= 630.99375 J
Therefore, the change in internal energy of the air within the piston is approximately 630.99375 J.
To find the change in internal energy of the air within the piston, we need to consider 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.
The heat absorbed by the air within the piston is given as 555 J.
To find the work done by the system, we can use the formula:
Work = -Pext * ΔV
Where:
- Pext is the external pressure (given as 1.0 atm)
- ΔV is the change in volume (final volume - initial volume)
Given:
- Pext = 1.0 atm
- ΔV = 0.87 L - 0.12 L = 0.75 L
Next, we need to convert the volume to SI units and then convert the units of pressure to Pascals (Pa) since Joule (J) is the SI unit of energy.
1 atm is approximately equal to 101325 Pa.
1 L is equal to 0.001 m^3.
So, converting the volume and pressure:
ΔV = 0.75 L * 0.001 m^3/L = 0.00075 m^3
Pext = 1.0 atm * 101325 Pa/atm = 101325 Pa
Now, we can calculate the work done by the system:
Work = -Pext * ΔV
= -101325 Pa * 0.00075 m^3
= -75.99 J
Finally, we can calculate the change in internal energy:
Change in internal energy = Heat - Work
= 555 J - (-75.99 J)
= 555 J + 75.99 J
= 630.99 J
Therefore, the change in internal energy of the air within the piston is approximately 630.99 J.