Name: _________________________
Block: _____
Date:_____/_____/_____
Specific Heat Capacity Problems (644)
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 cwater = 1 cal/(g°C) = 1 cal/(g⋅K)
o cwater = 4.184 J/(g°C) = 4.184 J/(g⋅K)
o cwater = 4184 J/(kg°C) = 4184 J/(kg⋅K)
!
1. How many calories of heat will need to be added to a 200 g sample of water to raise
its temperature 30°C? (cwater = 1 cal/(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
Q = mc"T
2. Randy has a 500 g of water at 20°C. If he wants the final temperature of the water
to be 75°C (the change in temperature will be 55°C), how many Joules of heat will
he need to add? (cwater = 4.184 J/(g°C)
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
!
Formula
Q = mc"T
Quantities
“plugged in” &
Work
Answer, with
units
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?
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
Q = mc"T
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?
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
!
Formula
Q = mc"T
Quantities
“plugged in” &
Work
Answer, with
units
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?
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
Q
c=
m"T
6. 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?
Knowns: (place a ? in the
unknown space, fill in
the others with the
appropriate quantity)
Q
=
____________
m
=
____________
c
=
____________
ΔT
=
____________
!
Formula
Q
"T =
mc
Quantities
“plugged in” &
Work
Answer, with
units
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?
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
Q
c=
m"T
8. What mass of water will give up 240 calories when its temperature drops from 12°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
Q
m=
c"T