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 _____

Options

A. less than `50^@ C` but greater than `0^@C`
B. `0^@C`
C. `50^@C`
D. more than `50^@C`

Answer

D

Explanation

Suppose, `theta` is the final common temperature, moreover `S_c` and `S_h` respectively are the heat capacities of cold and hot bodies, where `S_c gt S_h`
According to principle of calorimetry,
Heat loss = heat gain
`S_h[100^@C-theta]=S_c theta`
`therefore S_h xx 100^@ -S_h xx theta =S_c theta`
`therefore S_h xx 100^@ =(S_h +S_c)theta`
`therefore theta =(S_h/(S_h+S_c))xx100^@`
`therefore theta = 1/(1+S_c/S_h)xx100^@` ...(1)
but `S_c lt S_h rArr S_c/S_h lt 1`
`rArr 1+ S_c/S_h lt 1+1`
`rArr 1+ S_c/S_h lt 2`
`therefore` From equation (1),
`theta gt 100^@/2`
`therefore theta gt 50^@C`