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mass of thermometer=0.055 kg
heat capacity=46.1 J/K
initial temperature=15°C
final temperature=44.4°C
mass of water=0.300 kg
heat capacity of water=4.2 J/K
initial temperature=T(let)
final temperature=44.4°C
now,
use concept of calorimetry,
Heat loss=Heat gain
here water is at higher temperature, so heat loss by water.and heat gain by thermometer.
heat loss by water=Mw×Cw×(Ti-44.4)
=0.3×4190×(Ti-44.4)
[Cw=4190 j/kg.K]
heat gain by thermometer=Mt×(St/Mt)×(44.4-15°)=St×29.4°
[ (St/Mt)=46.1 J/K is known as heat capacity ]
hence,
0.3×4190×(Ti-44.4°)=46.1×29.1
(Ti-44.4°)=46.1×29.4/0.3×4190
(Ti-44.4°)=1.07°C
Ti=44.4+1.07=45.47°C=45.5°C
Hence water insertion temperature is 45.5°C
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