Block: _____
Date:__________
Specific Heat Capacity Problems
Q = mc"T
Where:
Q = heat (“Quantity” of heat; aka: Thermal 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 (thermal or 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:
cal
cal
=1
g°C
gK
J
J
=1
o c water = 4.184
g°C
gK
J
J
=1
o c water = 4184
kg°C
kgK
o
!
c water = 1
!
1. How many calories of heat will need to be added to a 200 g sample of water to raise
! temperature 30°C?
its
m = 200g
Q = mc"T
"T = 30°C
cal
c =1
g # °C
Q?
!
$ cal '
Q = (200 g/ ) # &1
) # ( 30°C/ )
% g/ °C/ (
Q = 6000 cal
!
2. Randy has a 500 g of water at 20°C. If he wants the final temperature of the water
to be 75°C, how many Joules of heat will he need to add?
3. The element hydrogen has the highest specific heat of all elements. Hydrogen’s
specific heat capacity is 14300J/(kg K). If the temperature of a .34kg sample of
hydrogen is to be raised by 25 K, how much heat will have to be transferred to the
hydrogen?
4. Radon’s specific heat capacity is 94J/(kg K). If the temperature of a .34kg sample of
radon is to be raised by 25K, how much heat will have to be transferred to the
radon?
5. Harry has a 50 g lump of unknown material. He experiments with the material and
determines that the temperature of the substance increases by 6°C when 20 cal of
heat are added. What is the substance’s specific heat?
6. A .59 kg brass candlestick has an initial temperature of 98.0°C. If 21,100J of heat is
removed from the candlestick to lower its temperature to 6.8°C, what is the specific
heat capacity of brass?
7. Mercury has one of the lowest specific heat capacities. If 257J of heat are added to
.45 kg of mercury, the mercury’s temperature will increase by 4.09K. What is the
specific heat capacity of mercury?
Block: _____
Date:__________
Specific Heat Capacity Problems
Q = mc"T
Where:
Q = heat (“Quantity” of heat; aka: Thermal 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 (thermal or 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:
cal
cal
=1
g°C
gK
J
J
= 4.184
o c water = 4.184
g°C
gK
J
J
= 4184
o c water = 4184
kg°C
kgK
o
!
!
!
c water = 1
1. A .38kg drinking glass is filled with a hot liquid. The liquid transfers 7032J of heat
to the glass. If the temperature of the glass increases by 22K, what is the specific
heat capacity of the glass?
2. The specific heat capacity of glass is 0.20 cal/(g°C). If 30 cal of heat are added
to an unknown mass of glass, the temperature raises by 150°C. What is mass of
the glass?
3. What mass of water will give up 240 calories when its temperature drops from
80°C to 68°C.
4. If 216 J of energy is required to raise the temperature of aluminum from 15°C to
35°C, calculate the mass of aluminum. (specific heat of aluminum is 0.90 J/( g°C)
5. The temperature of air in a foundry increases when molten metals cool and
solidify. Suppose 9900000J of heat is added to the surrounding air by the
solidifying metal. The air’s temperature increases by 55K, and the air has a
specific heat capacity of 1000J/(kg K). What is the mass of the heated air?
6. 50 Joules of heat are added to a 2 kg block of iron. If the specific heat of iron is
452 J/(kg°C), how much will its temperature increase?
7. A 30 g piece of iron is dropped into a container of water and gives off 165
calories in cooling. Calculate the iron’s temperature change. (the specific heat
capacity of iron is 0.11 cal/( g°C)
8. The initial temperature of 150 g of ethanol was 22°C. What would be the final
temperature of the ethanol if 3,240 J of energy were added? The specific heat
capacity of ethanol is 2.44 J/ (g°C).