**Task 1: Cycle Process (3 Points)**
Consider the reversible cyclic process
for an ideal gas shown in Figure 1. In
step 4 → 1, the gas is compressed, at 1
→ 2 the gas extracts heat \(Q_2 \) from
a heat reservoir at temperature \(T_2 \)
during expansion, at 23 another
expansion occurs, during which the gas
releases heat \(Q_1 \) to a heat
reservoir at temperature \(T_1\),
followed by a compression at 3 → 4.
a) Calculate the amounts of heat
exchanged by the system at each part
of the cycle as a function of \(T_1\), \
(T_2 \), \(S_1\), and \(S_2 \).
b) What work \(W \) is performed by the
gas in one cycle? To return the entire
system to its initial state, heat extracted
from the hotter reservoir must be added
back (externally). The efficiency \(\eta
\) is defined as the ratio of the work
back (externally). The efficiency \(\eta
\) is defined as the ratio of the work
done to the heat extracted from the
hotter reservoir. Indicate \(\eta \) for the
cycle process.
c) What does the corresponding \(PV
1)-diagram for the cycle process look
like?
[Figure 1: a diagram showing a cyclic
process on a TS (Temperature-Entropy)
plot with states 1, 2, 3, and 4 connected
in sequence.]
T
2
T2
T
3
4
←
S
S2 S