\(n_{1}\) moles of an ideal monoatomic gas at temperature \(T_{1}\) and pressure \(P\) are in one compartment of an, insulated container. In an adjoining compartment, separated by an insulating partition three are \(n_{2}\) moles of another ideal monoatomic gas at temperature \(T_{2}\) and pressure \(P\). When the partition is removed, the final temperature of the mixture is

(a) \(\frac{n_{1}\left(T_{1}+T_{2}\right)}{\left(n_{1}+n_{2}\right)}\)

(b) \(\frac{\left(T_{1}+T_{2}\right)}{2}\)

(c) \(\frac{\left(n_{1} T_{1}+n_{2} T_{2}\right)}{\left(n_{1}+n_{2}\right)}\)

(d) \(\frac{\left(n_{1} T_{1}+n_{1} T_{2}\right)}{\left(n_{1}+n_{2}\right)}\)