if a gas is expanding,what will be the sign of the work done by it?
Positive, since the gas is doing positive work on the environment. The key word is 'by'. If, instead, you wanted the work done on the gas, it would be negative in the case of expansion.
Where a "sign convention" enters the picture is when talking simply about the work W in a thermodynamic process. For some people, books, etc., W means the work done by the system, W = PΔV, and the First Law of Thermodynamics is ΔU = Q - W. For others it means the work done on the system, W = -PΔV, and the First Law is ΔU = Q + W.
The common convention in science is that work done by the system is negative. This is understandable because work has units of energy and if a system does work he loses energy via ΔU = W = -PΔV (adiabatic process).
This is also the convention in engineering
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