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Two identical bodies are made of a mater...

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at `100^(@)C`. While the other one is at `0^(@)C`. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is

A

Less than `50^(@)C` but greater than `0^(@)C`

B

`0^(@)C`

C

`50^(@)C`

D

More than `50^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `theta` be the final common temperature. And `s_(b)` be the average heat capacities of the hot (initially) bodies respectively (where ) From, principle of calorimetry.
Heat lost = Heat gained
`s_(b)(100-theta)=s_(c)theta`
`thereforetheta=s_(b)/((s_(b)+s_(c)))xx100^(@)C=(100^(@)C)/((1+s_(c)/(s_(b))))`
`becauses_(c)//s_(b)lt1`
`therefore1+s_(c)//s_(b)lt2`
`thereforethetagt(100^(@)C)/(2)orthetagt50^(@)C`
or
Body at `100^(@)C` has more heat capacity then body so final temperature must be greater than `50^(@)C`.
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