Answer: q
=
64 kJ
Explanation:
As you know, a substance's specific heat tells you how much heat is required to increase the temperature of
1 g
of that sample by
1
∘
C
.
In water's case, you know that its specific heat is equal to
4.18
J
g
∘
C
. This tells you that in order to increase the temperature of
1 g
of water by
1
∘
C
, you need to supply
4.18 J
of heat.
How much heat would you need to increase the temperature of
200 g
of water by
1
∘
C
?
Well, if you need
4.18 J
per gram to increase its temperature by
1
∘
C
, it follows that you will need
200
times more heat to get this done.
Likewise, if you were to increase the temperature of
1 g
of water by
76
∘
C
, you'd need
76
times more heat than when increasing the temperature of
1 g
by
1
∘
C
.
Combine these two requirements and you get the total amount of heat required to increase the temperature of
200 g
of water by
76
∘
C
.
Mathematically, this is expressed using the following equation
q
=
m
⋅
c
⋅
Δ
T
, where
q
- heat absorbed/lost
m
- the mass of the sample
c
- the specific heat of the substance
Δ
T
- the change in temperature, defined as final temperature minus initial temperature
Plug in your values to get
q
=
200
g
⋅
4.18
J
g
∘
C
⋅
(
100
−
24
)
∘
C
q
=
63536 J
I'll leave the answer rounded to two sig figs and expressed in kilojoules
q
=
64 kJ
