A gas is allowed to expand in a well insulated container against a con...
For insulated container dq=0,so du=dw =-pdv=2.5(4.5-2.5)=5litre atm and 1litre atm = 101.3joule so -5 *101-505 joule
A gas is allowed to expand in a well insulated container against a con...
Given:
- External pressure (P) = 2.5 atm
- Initial volume (V1) = 2.50 L
- Final volume (V2) = 4.50 L
To find:
Change in internal energy (ΔU) in joules
Formula:
The change in internal energy of a system can be calculated using the formula:
ΔU = q + w
where,
- ΔU = change in internal energy
- q = heat transferred to the system
- w = work done by the system
Explanation:
In this case, the container is well insulated, which means there is no heat transfer between the system (gas) and the surroundings. Therefore, q = 0.
The work done by the system can be calculated using the formula:
w = -PΔV
where,
- P = external pressure
- ΔV = change in volume
Step 1: Calculate the change in volume (ΔV)
ΔV = V2 - V1
= 4.50 L - 2.50 L
= 2.00 L
Step 2: Calculate the work done (w)
w = -PΔV
= -(2.5 atm)(2.00 L)
= -5.00 atm L
Step 3: Calculate the change in internal energy (ΔU)
ΔU = q + w
= 0 + (-5.00 atm L)
To convert atm L to joules, we can use the conversion factor:
1 atm L = 101.3 J
Therefore,
ΔU = (-5.00 atm L) x (101.3 J/atm L)
= -505 J
Conclusion:
The change in internal energy of the gas is -505 J. Therefore, the correct answer is option C) -505 J.
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