question_answer 14)

ln an experiment on the specific heat of a metal, a 0.20 kg block of the metal at \[{{150}^{o}}C\] is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing \[150\,c{{m}^{3}}\] of water at \[{{27}^{o}}C\]. The final temperature is \[{{40}^{o}}C\]. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value of specific heat of the metal?

Answer:

Here, mass of metal, \[\vartriangle T=\frac{\vartriangle Q}{mc}\] Fall in temperature of metal \[=\frac{7\cdot 5\times {{10}^{5}}}{8\times {{10}^{3}}\times 0\cdot 91}={{11103}^{o}}C\] If c is specific heat of the metal, then heat lost by the metal, \[2\cdot 5\] Volume of water \[=150\,c.c.\] \[\therefore \] Mass of water, \[m'=150\,g\] ..(i) Water equivalent of calorimeter, \[0\cdot 39J{{g}^{-1}}\] Rise in temp. of water and calorimeter, \[^{o}{{C}^{-1}}.\] Heat gained by water and calorimeter, \[=335J{{g}^{-1}}.\]\[m=2\cdot 5kg=2500g\] \[\vartriangle T=500-0={{500}^{o}}C\]\[c=0\cdot 39J{{g}^{-1}}\] ..(ii) \[L=335J{{g}^{-1}}\] From (i) and (ii) \[\therefore \] or \[m'L=mc\vartriangle T\] If some heat is lost t0 the surroundings, value of c so obtained will be less than the actual value of c.