Explain sign convention of work during expansion and compression. OR�

1.	Explain sign convention of work during expansion and compression. OR Explain +W and -W.
Answer» (A) Expansion of a gas : (1) When a gas expands against a constant pressure, P_ex changing the volume from initial volume V₁ to final volume V₂, Change in volume, ΔV = V₂ - V₁ The mechanical work = W = -P_ex × ΔV = -P_ex(V₂ – V₁) (2) During expansion V₂ > V₁. The work is said to be performed by the system on the surroundings. This results in the decrease in the (work) energy of the system. Hence the work is negative, i.e. W is -ve. (B) Compression of a gas : During compression, V₂ < V₁. The work is said to be performed on the system by the surroundings. This results in the increase in the (work) energy of the system. Hence the work is positive, i.e. W is + ve.

Explain sign convention of work during expansion and compression. OR Explain +W and -W.

Answer»

(A) Expansion of a gas :

(1) When a gas expands against a constant pressure, P_ex changing the volume from initial volume V₁ to final volume V₂,

Change in volume,

ΔV = V₂ - V₁

The mechanical work = W = -P_ex × ΔV

= -P_ex(V₂ – V₁)

(2) During expansion V₂ > V₁. The work is said to be performed by the system on the surroundings. This results in the decrease in the (work) energy of the system. Hence the work is negative, i.e. W is -ve.

(B) Compression of a gas :

During compression, V₂ < V₁. The work is said to be performed on the system by the surroundings. This results in the increase in the (work) energy of the system. Hence the work is positive, i.e. W is + ve.

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