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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)
The amount of heat transferred from metal to water.
Answer to Problem 4SP
The amount of heat transferred from metal to water is
Explanation of Solution
Given info: A
Write the expression for heat in terms of specific heat capacity
Here,
Write the expression for change in temperature
Here,
Substitute equation (2) in (1)
Substitute
Conclusion:
The amount of heat transferred from metal to water is
(b)
The specific heat capacity of metal.
Answer to Problem 4SP
The specific heat capacity of metal is
Explanation of Solution
Given info: A
Write the expression for specific heat capacity of metal
Substitute
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
(c)
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
Explanation of Solution
Given info: A
Write the expression for heat in terms of specific heat capacity
Here,
Write the expression for change in temperature
Here,
Substitute equation (2) in (1)
Substitute
Write the expression of mass in terms of specific heat capacity
Substitute
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
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