Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 14, Problem 13P
To determine

Equilibrium temperature of copper in an aluminium and water calorimeter.

Expert Solution & Answer
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Answer to Problem 13P

Solution:

Equilibrium temperature of copper in an aluminium and water calorimeter is 75.3 C

Explanation of Solution

Given:

cpa is the specific heat of copper which is 376 J/kgk

cpb is the specific heat of aluminium which is 921 J/kgk

cpc is the specific heat of water which is 4186 J/kgk

ma is the mass of copper which is 265 g or 0.265 kg

mb is the mass of aluminium which is 145 g

mc is the mass of water which is 825 g or 0.825 kg

Ta is the temperature of copper which is 245 C

Tb is the temperature of aluminium which is 12 C

Tc is the temperature of water which is 12 C

Formula Used:

The formula used is the relation between temperature and specific heat from thermodynamics

Q=mcp(TfTi)

Where,

Q is the heat transferred

cp is the specific heat

m is the mass

Tf is the final temperature

Ti is the initial temperature

From the formula above, the equilibrium temperature formula for calorimetry can be derived.

If two materials a, b and calorimeter c with temperatures Ta, Tb and Tc are in contact, then they will reach an equilibrium temperature Te.

This equilibrium temperature Te is given by equating the heat transferred by the three materials.

Qa=macpa(TeTa)

Qb=mbcpb(TeTb)

Qc=mccpc(TeTc)

Equating the heat transferred is Qa=(Qb+Qc)

This becomes

Qa=macpa(TeTa)=QbQc=mbcpb(TeTb)mccpc(TeTc)

macpa(TeTa)=mbcpb(TeTb)mccpc(TeTc)

macpa(TeTa)=mbcpb(TbTe)+mccpc(TcTe)

Te=macpa(Ta)+mbcpb(Tb)+mccpc(Tc)macpa+mbcpb+mccpc

Where,

cpa is the specific heat of material a

cpb is the specific heat of material b

cpc is the specific heat of material c

ma is the mass of material a

mb is the mass of material b

mc is the mass of material c

Ta is the temperature of material a

Tb is the temperature of material b

Tc is the temperature of material c

Te is equilibrium temperature

Calculation:

Inserting the given values in the equilibrium temperature formula for calorimetry:

Te=macpa(Ta)+mbcpb(Tb)+mccpc(Tc)macpa+mbcpb+mccpc

Te=(0.265)(376)(245)+(0.145)(921)(12)+(0.825)(4186)(12)(0.265)(376)+(0.145)(921)+(0.825)(4186)

Te=75.3 C

Chapter 14 Solutions

Physics: Principles with Applications

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