Physics 53
Summer 2010
Quiz 9
Solutions
Check the best answer.
1.
A container to keep liquids hot (or cold) consists of a bottle
as shown, with a double wall. The space between the walls
is a near vacuum, and the walls are made highly reflective
by silvering. Which of the following is true?
Vacuum
Silvered
The silvering reduces heat transfer by conduction.
The vacuum reduces heat transfer by radiation.
√
The vacuum reduces heat transfer by conduction.
The silvering reduces heat transfer by convection.
Check T or F depending on whether the statement is true or false.
2.
To increase the temperature of an ideal gas by the amount ΔT , the heat input
required is the same regardless of the process used.
T
√
F
1
Physics 53
3.
Summer 2010
One mole of an ideal gas ( cV = 32 R ) starts with pressure P0 and volume V0 . It is
expanded to volume 2V0 while keeping the quantity P ⋅ (3V0 − V ) constant.
a.
What is the final pressure?
b.
Find the initial and final temperatures and ΔEint for the process.
c.
Find the work done by the gas and the heat input.
[In finding the work, make the substitution x = 3V0 − V in the integral.]
a.
We have P0 ⋅ 2V0 = P ⋅V0 , or P = 2P0 .
b.
The initial temperature is T0 = P0V0 /R ; the final temperature is
T = 2P0 ⋅ 2V0 /R = 4T0 . This gives ΔEint = cV ΔT = 32 R ⋅ 3T0 = 92 P0V0 .
c.
The work is W = 2P0V0 ∫
2V0
V0
W = 2P0V0 ∫
2V0
V0
dV
. Making the suggested substitution we have
3V0 − V
dx
= 2P0V0 ln(2) . The heat input is Q = ΔEint + W = P0V0 ( 92 + ln 2) .
x
2