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Ms. Rasetti’s IP 614
Name: ________________________
Block: _____
Date:__________
Specific Heat Capacity Problems: Part 2
Q = mc"T
Where:
Q = heat (“Quantity” of heat; aka: Energy)
m = mass
c = specific heat
ΔT = change in temperature
A few key ideas:
 If a substance receives heat and experiences an increase in temperature then Q is a
positive number and ΔT is a positive number.
 If a substance loses heat and experiences a decrease in temperature then Q is a
negative number and ΔT is a negative number.
 Q (heat energy) can be measured in either Joules or calories. Just make sure that your
units for c are consistent with your units for Q.
 ΔT, change in temperature, can be measured in K, °C, or °F. Just make sure that your
units for c are consistent with your units for ΔT.
 Always start a problem by listing the given information (with units) and writing down the
specific heat capacity equation (without plugging numbers in yet!)
 You must ALWAYS show all work and make sure you have consistent units on your final
answer.
 The First Law of Thermodynamics states that if two substances exchange heat, the
quantity of heat gained by one substance is exactly equal and opposite to the quantity of
heat lost by the other substance.
 The specific heat capacity of water is:
o c water = 1 cal = 1 cal
g°C
gK
J
J
o c water = 4.184
= 4.184
g°C
gK
J
J
o c water = 4184
!
= 4184
kg°C
kgK
!
!
1. You have 125 milliliters (125 grams) of water at 10°C. You want to warm the water to 90°C to make
hot cocoa. How much heat do you have to add? [The specific heat capacity of water is 1
!
calorie/(g°C)]
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
2. You are trying to determine the identity of an unknown piece of metal (that has a mass of 25
grams). To help in identifying the metal, you decide to find out the material’s specific heat.
To do this, you place the unknown metal in a cold bath. The temperature of the cold bath
(and, therefore, the initial temperature of the unknown metal) is 5°C. You then fill an
insulated cup with 50 g of 90°C water and add the unknown material. The two reach a final
temperature of 86°C. [The specific heat capacity of water is 1 calorie/(g°C)]
a. First, you need to calculate the amount of heat the water loses:
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
b. Second, you can calculate the unknown material’s specific heat (HINT: the metal gains
the heat the water loses):
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
3. You are trying to determine the identity of an unknown material (that has a mass of 200
grams). To help in identifying the material, you decide to find out the material’s specific heat.
To do this, you place the unknown metal in a hot bath. The temperature of the hot bath
(and, therefore, the initial temperature of the unknown material) is 90°C. You then fill an
insulated cup with 100 g of 5°C water and add the unknown material. The two reach a final
temperature of 12°C. [The specific heat capacity of water is 1 calorie/(g°C)]
a. First, you need to calculate the amount of heat the water gains:
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
b. Second, you can calculate the unknown material’s specific heat (HINT: the material
loses the heat the water gains):
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
4. You are trying to determine the identity of an unknown piece of metal (that has a mass of 50
grams). To help in identifying the metal, you decide to find out the material’s specific heat.
To do this, you place the unknown metal in a cold bath. The temperature of the cold bath
(and, therefore, the initial temperature of the unknown metal) is 0°C. You then fill an
insulated cup with 100 g of 80°C water and add the unknown material. The two reach a final
temperature of 75°C. [The specific heat capacity of water is 1 calorie/(g°C)]
a. First, you need to calculate the amount of heat the water loses:
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
b. Second, you can calculate the unknown material’s specific heat (HINT: the metal gains
the heat the water loses):
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
Formula
Quantities
“plugged in” &
Work
Answer, with
units
5. A 0.225kg sample of tin, which has a specific heat capacity of 2300 J/(kg K), is
cooled in water. The amount of heat transferred to the water is 3900 J.
a. What is the change in temperature of the tin?
b. If the final temperature of the tin is 18°C, what was its initial temperature?
6. Tantalum is an element that is used in aircraft parts. Tantalum has a specific heat
capacity of about 140J/(kg K). The aircraft part has a mass of 0.23kg and is cooled
from a temperature of 1200K by being placed in water. If 30000J of heat is
transferred to the water, what is the final temperature of the part? (HINT: First
determine the change in temperature of the part.)
7. You are trying to identify an unknown metal. After learning about specific heat in
physics class, you know how to determine a material’s specific heat capacity, which
could be used in helping to determine the material’s identity.
a. You place the unknown material in 200 grams of water at 90°C and the
temperature of the water drops to 85.7°C. If water has a specific heat capacity of
1 calorie/(g°C), how much heat did the water lose?
b. If the unknown material has a mass of 100 grams and increases in temperature
from 5.7°C to 85.7°C, what is its specific heat capacity? (assume the material
gains all the heat lost by the water)
8. The temperature of the air above coastal areas is greatly influenced by the large
specific heat capacity of water. The specific heat of air is about 1000J/(kg K) .
Consider the situation where 4186J of heat is given up by 1kg of water causing its
temperature to drop by 1.0K. If the air over the water increases temperature by 5.5K,
what is its mass?
9. A handful of lead shot (specific heat 0.130 J/(g⋅°C) is heated to 95°C and dumped
into 230 g of cold water at a temperature of 18°C. The mixture comes to thermal
equilibrium at 32°C. What is the mass of the lead?
10. To determine the specific heat of a metal, 650 g of the metal are heated to 100°C
and dropped into 240 g of water at 17°C. If the mixture reaches equilibrium at 38°C,
what is the specific heat of the metal?
Challenge Problems: For an extra challenge, please try the following problems. If you
want to take Honors Chemistry, we EXPECT you to do these problems.
11. Phoebe’s insulated foam cup is filled with 0.150kg of coffee (c=4187J/kg°C) that is
too hot to drink so she adds 0.01kg of milk (c=3800J/(kg°C)) at 5.0°C. If the coffee
has an initial temperature of 70 °C, how hot is the coffee after the milk is added?
(What is the final temperature of the coffee and milk mixture?)
Heat lost by the coffee
-Qcoffee
-mcofccofΔTcof
-mcofccof(Tcof,f - Tcof,i)
-mcofccof(Tf - Tcof,i)
-(.150kg)(4187 J/ kg°C)( Tf - 70 °C)
-(628.05 J/°C) ( Tf - 70 °C)
-(628.05 J/°C) ( Tf ) + 43963.5 J
-43963.5 J
-(628.05 J/°C) ( Tf )
-(38 J/°C) ( Tf )
(-666.05 J/°C) ( Tf )
÷(-666.05 J/°C)
Tf
=
=
=
=
=
=
=
=
=
=
=
Heat gained by the milk
Qmilk
mmilkcmilkΔTmilk
mmilkcmilk(Tmilk,f – Tmilk,i)
mmilkcmilk(Tf – Tmilk,i)
(.01kg)(3800 J/ kg°C)( Tf - 5 °C)
(38 J/°C) ( Tf - 5 °C)
(38 J/°C) ( Tf ) – 190 J
-43963.5 J
(38 J/°C) ( Tf ) – 44153.5 J
-(38 J/°C) ( Tf )
- 44153.5 J
÷(-666.05 J/°C)
66.3 °C
12. Emily is testing her baby’s bath water and finds that it is too cold so she adds some
hot water from a kettle on the stove. If Emily adds 2.00kg of hot water at 80°C to
20kg of bath water at 27°C, what is the final temperature of the bath water? (water
c=4187J/kg°C)
13. Sidney is home from school with a cold, so mom has made him a bowl of chicken
soup (c=4187J/kg°C) which she ladles from a pot into a glass bowl. If .6kg of soup at
90°C is placed in a .2kg glass bowl (c=840J/kg°C) that is initially at 20°C, what will
be the temperature of the soup when the soup and the bowl have reached
equilibrium?
14. Nila is emptying the dishwasher. He removes a .2kg glass that has a temperature of
30°C (c=840J/kg°C). Into it he pours .1kg of diet soda (c=4187J/kg°C) which comes
out of the fridge at 5°C. Assuming no external heat loss, what is the final equilibrium
temperature of the glass of diet soda?