Physics of Everyday Phenomena
Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
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Chapter 10, Problem 4SP

A 170-g quantity of a certain metal, initially at 125°C, is dropped into an insulated beaker containing 84 g of water at 16°C. The final temperature of the metal and water in the beaker is measured as 39°C. Assume that the heat capacity of the beaker can be ignored.

a.    How much heat has been transferred from the metal to the water?

b.    Given the temperature change and mass of the metal, what is the specific heat capacity of the metal?

c.    If the final temperature of the water and this metal is 53°C instead of 39°C, what quantity of this metal (initially at 125°C) was dropped into the insulated beaker?

(a)

Expert Solution
Check Mark
To determine

The amount of heat transferred from metal to water.

Answer to Problem 4SP

The amount of heat transferred from metal to water is 1932cal.

Explanation of Solution

Given info: A 170g quantity of a certain metal, initially at 125°C , is dropped into an insulated beaker containing 84 g of water at 16°C . The final temperature of the metal and water in the beaker is measured as 39°C.

Write the expression for heat in terms of specific heat capacity

Q=mcΔT (1)

Here,

Q is the heat

m is the mass

c is the specific heat capacity of ice

ΔT is the change in temperature

Write the expression for change in temperature

ΔT=T2T1 (2)

Here,

ΔT is the change in temperature

T1 is the initial temperature

T2 is the final temperature

Substitute equation (2) in (1)

Q=mc(T2T1) (3)

Substitute 84g for m, 1cal/g°C for c, 16°C for T1 and 39°C for T2 in equation (3)

Q=84g×1cal/g°C(39°C16°C)=1932cal

Conclusion:

The amount of heat transferred from metal to water is 1932cal.

(b)

Expert Solution
Check Mark
To determine

The specific heat capacity of metal.

Answer to Problem 4SP

The specific heat capacity of metal is 0.132cal/g°C.

Explanation of Solution

Given info: A 170g quantity of a certain metal, initially at 125°C , is dropped into an insulated beaker containing 84 g of water at 16°C . The final temperature of the metal and water in the beaker is measured as 39°C.

Write the expression for specific heat capacity of metal

c=Qm(T2T1)

Substitute 170g for m, 1932cal for Q, 125°C for T1, and 39°C for T2 in the above equation

c=1932cal170g(39°C125°C)=1932cal170g×(86°C)=0.132cal/g°C

The negative sign in the above expression is avoided since specific heat capacity is a positive quantity.

Conclusion:

The specific heat capacity of metal is 0.132cal/g°C.

(c)

Expert Solution
Check Mark
To determine

The quantity of heat was dropped from metal to insulating beaker.

Answer to Problem 4SP

The quantity of heat was dropped from metal to insulating beaker is 327g.

Explanation of Solution

Given info: A 170g quantity of a certain metal, initially at 125°C , is dropped into an insulated beaker containing 84 g of water at 16°C . The final temperature of the metal and water in the beaker is measured as 39°C.

Write the expression for heat in terms of specific heat capacity

Q=mcΔT (1)

Here,

Q is the heat

m is the mass

c is the specific heat capacity of ice

ΔT is the change in temperature

Write the expression for change in temperature

ΔT=T2T1 (2)

Here,

ΔT is the change in temperature

T1 is the initial temperature

T2 is the final temperature

Substitute equation (2) in (1)

Q=mc(T2T1) (3)

Substitute 84g for m, 1 cal/g°C for c, 16°C for T1 and 53°C for T2 in equation (3)

Q=84g×1cal/g°C(53°C16°C)=3108cal

Write the expression of mass in terms of specific heat capacity

m=Qc(T2T1) (4)

Substitute 0.132cal/g°C for c, 3108cal for Q, 125°C for T1 and 53°C for T2 in equation (4)

m=3108cal0.132cal/g°C×(53°C125°C)=327g

The negative sign in the above equation is avoided since mass is always a positive quantity.

Conclusion:

The quantity of heat was dropped from metal to insulating beaker is 327g.

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Chapter 10 Solutions

Physics of Everyday Phenomena

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