When two non-identical ideal gases are mixed irreversibly, the change in entropy due to mixing will be

(a) \(\Delta S_{\text {mix }}=-N \sum x_{i} \ln x_{i}\)

(b) \(\Delta S_{\text {mix }}=N R \sum x_{i} \ln x_{i}\)

(c) \(\Delta S_{\text {mix }}=-N R \sum x_{i} \ln x_{i}\)

(d) \(\Delta S_{\text {mix }}=N \sum x_{i} \ln x_{i}\).