Physics

Physics

Problem

During a reversible adiabatic compression of an ideal gas, what are the signs of the work done by the gas (W)(W) and the change in its internal energy (ΔU)(\Delta U)? a) W>0,  ΔU>0W>0,\;\Delta U>0 b) W<0,  ΔU<0W<0,\;\Delta U<0 c) W<0,  ΔU>0W<0,\;\Delta U>0 d) W>0,  ΔU<0W>0,\;\Delta U<0
Intuitive explanation

In an adiabatic process, there's no heat exchange with surroundings, so the first law tells you that all work done on the gas must go directly into changing its internal energy. During compression, the gas is squeezed (work is done on it), so WW is negative by convention and ΔU\Delta U must be positive—the gas heats up internally. The key insight is that without heat escape, compression always raises internal energy.

Intuitive explanation

In an adiabatic process, there's no heat exchange with surroundings, so the first law tells you that all work done on the gas must go directly into changing its internal energy. During compression, the gas is squeezed (work is done on it), so WW is negative by convention and ΔU\Delta U must be positive—the gas heats up internally. The key insight is that without heat escape, compression always raises internal energy.

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