A 31.5-g glass thermometer reads 23.6°C before it is placed in 135 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 41 8°C. What was the original temperature of the water? Ignore the mass of fluid inside the glass thermometer.
Equilibrium temperature of a thermometer
Answer to Problem 14P
Solution:
Equilibrium temperature of a thermometer is 42.6 C.
Explanation of Solution
Given:
is the specific heat of glass which is 792 J/kgK
is the specific heat of water which is 4186 J/kgK
is the mass of glass which is 31.5 g
is the mass of water
is density of water is 1000 kg/cu.m
is volume which is 135 mL or 0.135 L
is the temperature of glass which is 23.6 C or 296.6 K
is the temperature of water
is equilibrium temperature which is 41.8 C or 314.8 K
Formula Used:
The formula used is the relation between temperature and specific heat from thermodynamics
Where,
is the heat transferred
is the specific heat
is the mass
is the final temperature
is the initial temperature
From the formula above, the equilibrium temperature formula can be derived.
If two materials and with temperatures and are in contact, then they will reach an equilibrium temperature .
This equilibrium temperature is given by equating the heat transferred by the two materials.
Equating the heat transferred is
This becomes
Where,
is the specific heat of material
is the specific heat of material
is the mass of material
is the mass of material
is the temperature of material
is the temperature of material
is equilibrium temperature
Calculation:
The mass of water is determined by the multiplying density with volume
Volume by the multiplying is 0.135 L. 1000 L is 1 cu.m. So 0.135 L is 0.000135 cu.m.
Mass is now
kg
Inserting the given values in the equilibrium temperature formula
K
C
Chapter 14 Solutions
Physics: Principles with Applications
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