Question

Chapter 12, Problem 043 Ideally, when a thermometer is used to measure the temperature of an object, the temperature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temperature will change. A thermometer has a mass of 28.7 9, a specific heat capacity of C-383 1/(kg C), and a temperature of 10.8 °C. It is immersed in 1719 of water, and the final temperature of the water and thermometer is 55.5 °C. What was the temperature of the water in degrees Celsius before the Insertion of the thermometer? Number Units the tolerance is +/-2%

Answer 1

(43) mass of thermometer m = 28.7 g = 0.0287 kg;

specific heat capacity of thermometer c = 883 J/(kg C)

specific heat capacity of water C = 4186 J/(kg C)

Initial temperature of thermometer T = 10.8 degree celcius

mass of water m' = 171 g = 0.171 kg

final temperature of system T' = 55.5 degree celcius

Let the initial temperature of water = T$_w$

Apply conservation of energy;

Heat gained by thermometer to reach equilibrium = Heat lost by water to reach equilibrium

$mc(T'-T)=-m'C\left ( T'-T_w \right )$

0.0287 x 883 x (55.5 - 10.8) = 0.171 x 4186 x (Tw - 55.5);

Tw = 57.0825 degree celcius