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 _____

Two identical bodies are made of a material for which the heat capacit

1.	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 _____
Answer» less than `50^@ C` but greater than `0^@C` `0^@C` `50^@C` more than `50^@C` Solution :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`