Question

An ideal gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 bar from an initial volume of 2.50 dm³ to a final volume of 4.50 dm³. The change in internal energy (∆U) of the gas will be ______.

Options

• +1136 J

• −1136 J

• −500 J

• +500 J

Answer 1

An ideal gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 bar from an initial volume of 2.50 dm³ to a final volume of 4.50 dm³. The change in internal energy (∆U) of the gas will be −500 J.

Explanation:

Work done in an irreversible process is given by:

W = −P_ext (V₂ − V₁)

= −2.5 bar × (4.50 − 2.50) dm³

= −5 bar dm³

= `-5  "dm"^3  "bar" xx 100 "J"/("dm"^3  "bar")`

= −500 J

As the system is insulated, no heat enters or leaves the system, i.e., Q = 0

∴ ∆U = Q + W

= 0 − 500 J

= −500 J