work - Thermodynamics - Sign convention

I use the sign convention:

• Heat absorbed by the system = $q+$ (positive)


• Heat evolved by the system = $q-$ (negative)


• Work done on the system = $w +$ (positive)


• Work done by the system = $w -$ (negative)

Could anyone please tell me, that volume increased in system does positive or negative work?

Answer

Volume increase in the system is due to work done by the system. Therefore W is negative using your notation. Think of it this way, work done on the system would push the system inwards, decreasing volume. Therefore a volume increase is work done by the system.

Alternatively you could reason using the formula: $dU = dQ - dW$ (using your notation conventions, were $U$ is internal energy, $W$ is work and $Q$ is heat added to the system)

$dW = PdV.$

Therefore

$dU = dQ - PdV$.

Therefore if $dV$ (change in volume) is positive, $dU$ (change in internal energy) is negative.