- #1
issacnewton
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Hi
I am trying this question from Physics gre prepbook
A heat pump is to extract from an outdoor environment at 7oC and heat the
environment indoors to 27 celcius. for each 15000 J of heat delivered indoors, the smallest
amount of work that must be supplied to the heat pump is approximately
a)500 J
b)1000 J
c)1100 J
d)2000 J
e) 2200 J
this is how I did my work.
[tex]T_c = (7+273) K[/tex]
[tex]T_h=(27+273) K[/tex]
the highest possible efficiency is that of carnot engine
[tex]\eta_{max}=1-\frac{T_c}{T_h}=\frac{1}{15}[/tex]
let the [itex]\eta[/itex] be the efficiency of this pump . then
[tex]\eta \leqslant \frac{1}{15}[/tex]
[tex]\because \; \eta=\frac{W_{eng}}{|Q_h|}[/tex]
[tex]\therefore \; \frac{W_{eng}}{|Q_h|} \leqslant \frac{1}{15}[/tex]
[tex]Q_h=15000 J\;\Rightarrow \; W_{eng}\leqslant \frac{15000}{15}[/tex]
[tex]W_{eng} \leqslant 1000 [/tex]
which suggests that W has some maximum value but the problem is talking about the
minimum value of W. is something wrong ?
I am trying this question from Physics gre prepbook
A heat pump is to extract from an outdoor environment at 7oC and heat the
environment indoors to 27 celcius. for each 15000 J of heat delivered indoors, the smallest
amount of work that must be supplied to the heat pump is approximately
a)500 J
b)1000 J
c)1100 J
d)2000 J
e) 2200 J
this is how I did my work.
[tex]T_c = (7+273) K[/tex]
[tex]T_h=(27+273) K[/tex]
the highest possible efficiency is that of carnot engine
[tex]\eta_{max}=1-\frac{T_c}{T_h}=\frac{1}{15}[/tex]
let the [itex]\eta[/itex] be the efficiency of this pump . then
[tex]\eta \leqslant \frac{1}{15}[/tex]
[tex]\because \; \eta=\frac{W_{eng}}{|Q_h|}[/tex]
[tex]\therefore \; \frac{W_{eng}}{|Q_h|} \leqslant \frac{1}{15}[/tex]
[tex]Q_h=15000 J\;\Rightarrow \; W_{eng}\leqslant \frac{15000}{15}[/tex]
[tex]W_{eng} \leqslant 1000 [/tex]
which suggests that W has some maximum value but the problem is talking about the
minimum value of W. is something wrong ?