The air was in a cylinder equipped with the piston absorbs 565 duels of heat and expands from an initial volume of .10 l to a final volume of .85 L against an external pressure of 1.0 ATM what is the change an internal energy of the air within the cylinder
To calculate the change in internal energy of the air within the cylinder, 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 the system minus the work (W) done by the system:
ΔU = Q - W
In this case, the air absorbs heat (Q) of 565 duels and expands against an external pressure of 1.0 ATM. To find the work done, we can use the equation:
W = PΔV
where P is the external pressure and ΔV is the change in volume.
Given:
Heat absorbed, Q = 565 duels
Initial volume, Vi = 0.10 L
Final volume, Vf = 0.85 L
External pressure, P = 1.0 ATM
First, let's calculate the change in volume:
ΔV = Vf - Vi
= 0.85 L - 0.10 L
= 0.75 L
Next, let's calculate the work done, W:
W = PΔV
= 1.0 ATM * 0.75 L
= 0.75 ATM.L
Now we can calculate the change in internal energy:
ΔU = Q - W
= 565 duels - 0.75 ATM.L
Please note that the units for ΔU will depend on the specific unit for heat (Q) used in your question. Make sure to use consistent units throughout your calculations.
To calculate the change in internal energy of the air within the cylinder, you can 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
In this case, the air absorbs heat (Q) and does work against an external pressure (W). The heat absorbed is given as 565 J (joules), and the external pressure is given as 1.0 ATM (atmosphere).
To obtain the work done by the system, you can use the formula:
W = PΔV
Where:
W = work done by the system
P = external pressure
ΔV = change in volume
Given that the external pressure (P) is 1.0 ATM and the change in volume (ΔV) is (0.85 L - 0.10 L), you can substitute these values into the formula to find the work done by the system.
W = (1.0 ATM) × (0.85 L - 0.10 L)
Next, convert the atmospheric pressure to the SI unit of pressure, which is the pascal (Pa). 1 atmosphere is equal to 101,325 pascals.
W = (101,325 Pa) × (0.85 L - 0.10 L) = (101,325 J/L) × (0.75 L)
Now, you have the work done by the system (W), which you can substitute into the first law of thermodynamics equation to find the change in internal energy (ΔU):
ΔU = Q - W = 565 J - (101,325 J/L × 0.75 L)
Simplify the calculation:
ΔU = 565 J - 75,994 J
Therefore, the change in internal energy of the air within the cylinder is:
ΔU = -75,429 J