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Question
Select the most appropriate option.
A gas is allowed to expand in a well-insulated container against a constant external pressure of 2.5 bar from an initial volume of 2.5 L to a final volume of 4.5 L. The change in internal energy, ΔU of the gas will be _______.
Options
–500 J
+ 500 J
–1013 J
+ 1013 J
Solution
- 500 J
Explanation:
Since the container is insulated, this is an adiabatic process.
For adiabatic process,
ΔU = +W = - Pext Δ V = - Pext (V2 - V1)
Initial volume (V1) = 2.5 L = 2.5 dm3
Final volume (V2) = 4.5 L = 4.5 dm3
External pressure (Pext) = 2.5 bar
ΔU = W = - 2.5 bar × (4.5 dm3 - 2.5 dm3)
= - 5.0 dm3 bar × `(100 "J")/(1 "dm"^3 "bar")`
= - 500 J
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