wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If 2 moles of an ideal monoatomic gas at temperature T0 is mixed with 4 moles of another ideal monoatomic gas at temperature 2T0 in a closed vessel, then the temperature of the mixture is

A
53T0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
32T0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
43T0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
54T0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

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.

flag
Suggest Corrections
thumbs-up
34
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon