Inquiry into Physics
Inquiry into Physics
8th Edition
ISBN: 9781337515863
Author: Ostdiek
Publisher: Cengage
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Chapter 5, Problem 44Q
To determine

To rank the final temperature of water after adding different containers.

Expert Solution & Answer
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Answer to Problem 44Q

The final temperature of water according to different added container is ranked from largest to smallest temperature.

T3>T2>T6>T4>T5>T1.

Explanation of Solution

Container A:

Given info:

The mass of water is 1500g.

The temperature of water is 24°C.

The mass of the container A is 100g and temperature is 30°C.

The specific heat value for copper is 0.385Jg1C°1.

The specific heat value for water is 4.184Jg1C°1.

Formula used:

Formula to find the Final equilibrium temperature:

As amount of heat lost by copper is equal to the amount of heat gained by water,

mc(TcT)scopper=mw(TTw)swater

Here, mc is the mass of copper, Tc is the initial temperature of the copper container A, T is the equilibrium temperature, scopper is the specific heat capacity of the copper. mw is the mass of water, Tw is the initial temperature of the water, T is the equilibrium temperature, swater is the specific heat capacity of the water.

Calculation:

Substitute the given values to find the final equilibrium temperature,

100g(30°CT1)0.385Jg1C°1=1500g(T124°C)4.184Jg1C°138.5(30°CT1)=6276(T124°C)(30°CT1)=163.013(T124°C)

After simplifying we get,

T1=24.04C°

Container B:

Given info:

The mass of water is 1500g.

The temperature of water is 24°C.

The mass of the container B is 200g and temperature is 60°C.

The specific heat value for copper is 0.385Jg1C°1.

The specific heat value for water is 4.184Jg1C°1.

Formula used:

Formula to find the Final equilibrium temperature:

As amount of heat lost by copper is equal to the amount of heat gained by water,

mc(TcT)scopper=mw(TTw)swater

Here, mc is the mass of copper, Tc is the initial temperature of the copper container A, T is the equilibrium temperature, scopper is the specific heat capacity of the copper. mw is the mass of water, Tw is the initial temperature of the water, T is the equilibrium temperature, swater is the specific heat capacity of the water.

Calculation:

Substitute the given values to find the final equilibrium temperature,

200g(60°CT2)0.385Jg1C°1=1500g(T224°C)4.184Jg1C°138.5(60°CT2)=6276(T224°C)(60°CT2)=81.51(T224°C)

After simplifying we get,

T2=24.43C°

Container C:

Given info:

The mass of water is 1500g.

The temperature of water is 24°C.

The mass of the container C is 300g and temperature is 90°C.

The specific heat value for copper is 0.385Jg1C°1.

The specific heat value for water is 4.184Jg1C°1.

Formula used:

Formula to find the Final equilibrium temperature:

As amount of heat lost by copper is equal to the amount of heat gained by water,

mc(TcT)scopper=mw(TTw)swater

Here, mc is the mass of copper, Tc is the initial temperature of the copper container A, T is the equilibrium temperature, scopper is the specific heat capacity of the copper. mw is the mass of water, Tw is the initial temperature of the water, T is the equilibrium temperature, swater is the specific heat capacity of the water.

Calculation:

Substitute the given values to find the final equilibrium temperature,

300g(90°CT3)0.385Jg1C°1=1500g(T324°C)4.184Jg1C°1115.5(90°CT3)=6276(T324°C)(90°CT3)=54.34(T324°C)

After simplifying we get,

T3=25.19C°

Container D:

Given info:

The mass of water is 1500g.

The temperature of water is 24°C.

The mass of the container D is 200g and temperature is 15°C.

The specific heat value for copper is 0.385Jg1C°1.

The specific heat value for water is 4.184Jg1C°1.

Formula used:

Formula to find the Final equilibrium temperature:

As amount of heat lost by copper is equal to the amount of heat gained by water,

mc(TcT)scopper=mw(TTw)swater

Here, mc is the mass of copper, Tc is the initial temperature of the copper container A, T is the equilibrium temperature, scopper is the specific heat capacity of the copper. mw is the mass of water, Tw is the initial temperature of the water, T is the equilibrium temperature, swater is the specific heat capacity of the water.

Calculation:

Substitute the given values to find the final equilibrium temperature,

200g(15°CT4)0.385Jg1C°1=1500g(T424°C)4.184Jg1C°177(15°CT4)=6276(T424°C)(15°CT4)=81.51(T424°C)

After simplifying we get,

T4=24.183C°

Container E:

Given info:

The mass of water is 1500g.

The temperature of water is 24°C.

The mass of the container E is 300g and temperature is 30°C.

The specific heat value for copper is 0.385Jg1C°1.

The specific heat value for water is 4.184Jg1C°1.

Formula used:

Formula to find the Final equilibrium temperature:

As amount of heat lost by copper is equal to the amount of heat gained by water,

mc(TcT)scopper=mw(TTw)swater

Here, mc is the mass of copper, Tc is the initial temperature of the copper container A, T is the equilibrium temperature, scopper is the specific heat capacity of the copper. mw is the mass of water, Tw is the initial temperature of the water, T is the equilibrium temperature, swater is the specific heat capacity of the water.

Calculation:

Substitute the given values to find the final equilibrium temperature,

300g(30°CT5)0.385Jg1C°1=1500g(T524°C)4.184Jg1C°1115.5(30°CT5)=6276(T524°C)(30°CT5)=54.34(T524°C)

After simplifying we get,

T5=24.11C°

Container F:

Given info:

The mass of water is 1500g.

The temperature of water is 24°C.

The mass of the container F is 100g and temperature is 60°C.

The specific heat value for copper is 0.385Jg1C°1.

The specific heat value for water is 4.184Jg1C°1.

Formula used:

Formula to find the Final equilibrium temperature:

As amount of heat lost by copper is equal to the amount of heat gained by water,

mc(TcT)scopper=mw(TTw)swater

Here, mc is the mass of copper, Tc is the initial temperature of the copper container A, T is the equilibrium temperature, scopper is the specific heat capacity of the copper. mw is the mass of water, Tw is the initial temperature of the water, T is the equilibrium temperature, swater is the specific heat capacity of the water.

Calculation:

Substitute the given values to find the final equilibrium temperature,

100g(60°CT6)0.385Jg1C°1=1500g(T624°C)4.184Jg1C°138.5(60°CT6)=6276(T624°C)(60°CT6)=163.013(T624°C)

After simplifying we get,

T6=24.22C°

After calculation the final temperature of water according to different added container is ranked from largest to smallest temperature as,

T3>T2>T6>T4>T5>T1.

Conclusion:

Thus, the final temperature of water is ranked from largest to smallest temperature as,

T3>T2>T6>T4>T5>T1.

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Chapter 5 Solutions

Inquiry into Physics

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