All Solutions
Page 406: Lesson Check
a) Resulting popcorn
b) Omelet
c) a pile of bricks
d) ash.
B($4.5%$),D($17.7%$),C($25%$),A($50%$).
$$
eta = 1-frac{T_c}{T_h} = 21%.
$$
$$
eta = 1-frac{T_c}{T_h}
$$
which yields
$$
T_c = (1-eta)T_h = 311.6text{ K}.
$$
$$
eta = frac{W}{Q_{received}} = frac{W}{Q_{exhausted} + W} = 28.1%.
$$
$$
frac{Q_c}{Q_h} = frac{T_c}{T_h}.
$$
Knowing that
$$
Q_h=W+Q_c
$$
we get
$$
frac{Q_c}{Q_c+W}=frac{T_c}{T_h}.
$$
Last two equations give us
$$
Q_c = Wfrac{T_c}{T_h-T_c} =1920text{ J}quad Q_h = 3120text{ J}
$$
so we need to add $Q_h = 3120text{ J}$
b) The heat discarded is simply
$$
Q_c=1920text{ J}.
$$
$$
begin{align*}
Delta S &= dfrac{text{heat}}{text{temperature}}\
\
Delta S &= dfrac{Q}{T}\
end{align*}
$$
First we need to find the heat:
$$
Q = m cdot L_f
$$
Where $L_f = -33.5 cdot 10^4 text{ }dfrac{text{J}}{text{kg}}$
And $m = 3.1 text{ kg}$
Therefore,
$$
begin{align*}
Q &= 3.1 cdot (-33.5 cdot 10^4)\
\
Q &= -103.85 cdot 10^4 text{ J}\
end{align*}
$$
Temperature is $T = 0^circtext{C}$ which can be written as $T = 273text{ K}$
The change in entropy will be:
$$
begin{align*}
Delta S &= dfrac{-103.85 cdot 10^4}{273}\
\
Delta S &= -3.8 cdot 10^3 text{ J}\
\
Delta S &= boxed{-3.8 text{ kJ}}\
end{align*}
$$
Delta S = -3.8 text{ kJ}
$$