Question

A thermometer of mass 0.075 kg and heat capacity 46.1 J/K reads 25.0°C. It is then completely immersed in 0.300 kg of water and it comes to the same final temperature as the water. If the thermometer reads 54.4°C, what was the temperature of the water berfore insertion of the thermometer, neglecting other heat losses?

Answer 1

Answer:

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 again 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 = 45.5°C