   # If water with a mass m k at temperature T k is poured into an aluminum cup of mass m A1 containing mass m c of water at T c , where T k &gt; T c , what is the equilibrium temperature of the system? ### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 19, Problem 6P
Textbook Problem
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## If water with a mass mk at temperature Tk is poured into an aluminum cup of mass mA1 containing mass mc of water at Tc, where Tk > Tc, what is the equilibrium temperature of the system?

To determine
The equilibrium temperature of the system.

### Explanation of Solution

Given info:The mass of the hot water is mh and the temperature is Th . The mass of the aluminum cup is mAl , the mass of the cold water is mc and temperature is Tc .

Formula to calculate the energy lost by the hot water is,

Qh=mhcw(ThT)

Here,

Qh is the energy lost of hot water.

T is the equilibrium temperature of system.

cw is the specific heat of water.

Formula to calculate the energy gained by aluminum cup is,

QAl=mAlcAl(TTc)

Here,

QAl is the energy gained by aluminum cup.

cAl is the specific heat of aluminum.

Formula to calculate the energy gained by cold water is,

Qc=mccw(TTc)

Here,

Qc is the energy gained by cold water.

From the conservation of energy,

Qh=QAl+Qcmhcw(ThT)=mAlcAl(Tx

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