A gas is allowed to expand in a well insulated container against constant external pressure of 2.5 atm from an initial volume of 2.50 L to a final volume of 4.50 L. The change in internal energy Δ U of the gas in joules will be: (A) +505 J (B) +1136.25 J (C) -500 J (D) -505 J

We know that,

Change in the internal energy is given by the following expression

ΔU = q + W

where

ΔU = change in internal energy of the system

q = heat transfer between the system

W = work done by the system

As per the question, given that the gas is allowed to expand in a well insulated container.

Hence, heat transfer i.e q = 0

So,

ΔU = W = -PΔV

ΔU = W = -2.5 atm x (4.50 L – 2.50 L)

ΔU = W = -5.0 L atm

Convert the unit to joule

ΔU = W = -5.0 L atm x (101.33 J/ 1 L atm)

We get,

ΔU = -505 J

Therefore, the correct option is (D)

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