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n' number of liquids of masses m,2m,3m,4...

n' number of liquids of masses `m,2m,3m,4m,` ….. Having specific heats `S,2S,3S,4S,`…. Are at temperatures `t,2t,3t,4t`…. Are mixed. The resultant temperature of mixture is

A

`(3n)/(2n+1)t`

B

`(2n(n+1))/(3(n+1))t`

C

`(3n(n+1))/(2(n+1))t`

D

`(3n(n+1))/((2n+1))t`

Text Solution

Verified by Experts

The correct Answer is:
C
From principle of calorimetry
`theta = (m_(1)S_(1)theta_(1)+m_(2)S_(2)theta_(2)+....)/(m_(1)S_(1)+ m_(2)S_(2)+....)`
`m_(2)=6.25 m_(1) , % = (m_(2))/(m_(1)+m_(2)) xx 100`
`theta = ((1^(3)+2^(3)+3^(3) +....+ n^(3))t)/((1^(2)+2^(2)+3^(2) + ....+n^(2)))`.
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