The correct option is A 53T0
Let 'n' be the total number of moles of the mixture of two gases.
Given,
Number of moles of monoatomic gas 1
(n1)=2 moles
Number of moles of monoatomic gas 2
(n2)=4 moles
Let T be the temperature of the mixture. Then,
Internal energy of the mixture of two gases is given by
U=U1+U2
⇒U=f2(n1RT1++n2RT2)
⇒n(fR2) T=fR2×n1×T0+fR2×n2×2T0 ...(1)
Number of moles of gas in the mixture (n)=n1+n2=2+4
Also, f=3 for monoatomic gas.
Using this in (1), we get
(2+4)T=2T0+8T0 (∵n1=2,n2=4)
∴T=53T0
Thus, option (a) is the correct answer.