13.5. Specific Heat http://www.ck12.org
Therefore, the temperature of the silver will go up by 1. 70 ◦Cfor every 1. 00 ◦Cincrease in temperature of the zinc.
b. The temperature of a zinc coin increases from 20. 0 ◦C to 25. 0 ◦Cafter absorbing heat. What is the final temperature
for a silver coin of the same mass at the same initial temperature which absorbs the same amount of heat?
Answer:( 5. 0 ◦C)( 1. 696 ) = 8. 48 → 8. 5 ◦Cincrease in the temperature for the silver. The final temperature is 28. 5 ◦C.
Calorimetry
If a system is insulated well for a period of time so that no appreciable energy is transferred beyond the system, we
can think of such a system as being nearly “isolated.” This means for an isolated system composed of two objects
with unlike temperatures, the hotter object will transfer energy to the colder object until the temperatures of both
objects are identical.
Since energy must be conserved, we can find the final temperature of an isolated system. The energy lost by some
of the objects must equal the energy gained by other objects. That is,
−Qlost=Qgained,Qlost< 0
The energy lost by the hotter object is equal to the energy received by the colder object.
Illustrative Example 2
Let us imagine an isolated system consisting of a 30-g block of zinc heated to 300. 0 ◦Cwhich is placed into contact
with a 30-g block of silver initially at a temperature of 20. 0 ◦C.
What is the final temperature of the system, after equilibrium is reached?
Answer:
The energy transferred by the zinc block is−Qlost=−czincmzinc∆Tzincand the energy received by the silver block
from isQgained=csilvermsilver∆Tsilver.
Thus,−czincmzinc∆Tzinc=csilvermsilver∆Tsilver. Butmzinc=msilver, so we can write:
−czinc∆Tzinc=csilver∆Tsilver
∆Tzinc=Tf− 300. 0 ◦C and∆Tsilver=Tf− 20. 0 ◦C
−czinc(Tf− 300. 0 ◦C) =csilver(Tf− 20. 0 ◦C)→
czincTf+csilverTf= ( 20. 0 ◦C)csilver+( 300. 0 ◦C)czinc→
Tf=(^20.^0
◦C)csilver+( 300. 0 ◦C)czinc
czinc+csilver =( 20. 0 ◦C)( (^230) kgJ◦C)+( 300 ◦C)( (^390) kgJ◦C)
( (^390) kgJ◦C+ (^230) kgJ◦C) →^196.^13 →^196
◦C
- The conversion from temperature expressed in Celsius to kelvin is
TK=TC
(
(^1) CK
)
+ 273 ◦Kor more simply→TK=TC+ 273- The relationship between the average kinetic energy of a gas and its temperature isKE=^12 m(vt)^2 =^32 kT,
wherevtis the mean translational velocity of the molecules,mis their mass,kthe Boltzmann constant, is equal to - 38 × 10 −^23 KJandTthe temperature is expressed in Kelvin.
- The internal energy can be directly related to the temperature of a gas asU=N
( 3
2 kT)
→U=^32 NkT- Energy that is transferred from one object to another object due to a temperature difference between the objects
is called heat. - The amount of energy required to raise the temperature of one gram of water by one degree Celsius is defined as
onecalorie, or, as it is sometimes referred to, one “small” calorie. The calorie is therefore a measure of energy and