2.118. Find the efficiency of a cycle consisting of two isobaric and
two adiabatic lines, if the pressure changes n times within the cycle.
The working substance is an ideal gas whose adiabatic exponent is
equal to y.
2.119. An ideal gas whose adiabatic exponent equals y goes through
a cycle consisting of two isochoric and two isobaric lines. Find the
efficiency of such a cycle, if the absolute temperature of the gas rises
n times both in the isochoric heating and in
the isobaric expansion.
7;
2.120. An ideal gas goes through a cycle
consisting of
(a) isochoric, adiabatic, and isothermal
lines;
(b) isobaric, adiabatic, and isothermal
lines,
with the isothermal process proceeding at
V
the minimum temperature of the whole cycle.
Find the efficiency of each cycle if the absolute temperature varies n-fold within the cycle.
2.121. The conditions are the same as in the foregoing problem
with the exception that the isothermal process proceeds at the maximum temperature of the whole cycle.
2.122. An ideal gas goes through a cycle consisting of isothermal,
polytropic, and adiabatic lines, with the isothermal process proceeding at the maximum temperature of the whole cycle. Find the efficiency of such a cycle if the absolute temperature varies n-fold within
the cycle.
2.123. An ideal gas with the adiabatic exponent y goes through
a direct (clockwise) cycle consisting of adiabatic, isobaric, and isochoric lines. Find the efficiency of the cycle if in the adiabatic process
the volume of the ideal gas
(a) increases n-fold; (b) decreases n-fold.
2.124. Calculate the efficiency of a cycle consisting of isothermal,
isobaric, and isochoric lines, if in the isothermal process the volume
of the ideal gas with the adiabatic exponent y
(a) increases n-fold; (b) decreases n-fold.
2.125. Find the efficiency of a cycle consisting of two isochoric and
two isothermal lines if the volume varies v-fold and the absolute
temperature r-fold within the cycle. The working substance is an
ideal gas with the adiabatic exponent y.
2.126. Find the efficiency of a cycle consisting of two isobaric and
two isothermal lines if the pressure varies n-fold and the absolute
temperature ti-fold within the cycle. The working substance is an
ideal gas with the adiabatic exponent y.
2.127. An ideal gas with the adiabatic exponent y goes through
a cycle (Fig. 2.3) within which the absolute temperature varies
t-fold. Find the efficiency of this cycle.
2.128. Making use of the Clausius inequality, demonstrate that
Fig. 2.2.
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two adiabatic lines, if the pressure changes n times within the cycle.
The working substance is an ideal gas whose adiabatic exponent is
equal to y.
2.119. An ideal gas whose adiabatic exponent equals y goes through
a cycle consisting of two isochoric and two isobaric lines. Find the
efficiency of such a cycle, if the absolute temperature of the gas rises
n times both in the isochoric heating and in
the isobaric expansion.
7;
2.120. An ideal gas goes through a cycle
consisting of
(a) isochoric, adiabatic, and isothermal
lines;
(b) isobaric, adiabatic, and isothermal
lines,
with the isothermal process proceeding at
V
the minimum temperature of the whole cycle.
Find the efficiency of each cycle if the absolute temperature varies n-fold within the cycle.
2.121. The conditions are the same as in the foregoing problem
with the exception that the isothermal process proceeds at the maximum temperature of the whole cycle.
2.122. An ideal gas goes through a cycle consisting of isothermal,
polytropic, and adiabatic lines, with the isothermal process proceeding at the maximum temperature of the whole cycle. Find the efficiency of such a cycle if the absolute temperature varies n-fold within
the cycle.
2.123. An ideal gas with the adiabatic exponent y goes through
a direct (clockwise) cycle consisting of adiabatic, isobaric, and isochoric lines. Find the efficiency of the cycle if in the adiabatic process
the volume of the ideal gas
(a) increases n-fold; (b) decreases n-fold.
2.124. Calculate the efficiency of a cycle consisting of isothermal,
isobaric, and isochoric lines, if in the isothermal process the volume
of the ideal gas with the adiabatic exponent y
(a) increases n-fold; (b) decreases n-fold.
2.125. Find the efficiency of a cycle consisting of two isochoric and
two isothermal lines if the volume varies v-fold and the absolute
temperature r-fold within the cycle. The working substance is an
ideal gas with the adiabatic exponent y.
2.126. Find the efficiency of a cycle consisting of two isobaric and
two isothermal lines if the pressure varies n-fold and the absolute
temperature ti-fold within the cycle. The working substance is an
ideal gas with the adiabatic exponent y.
2.127. An ideal gas with the adiabatic exponent y goes through
a cycle (Fig. 2.3) within which the absolute temperature varies
t-fold. Find the efficiency of this cycle.
2.128. Making use of the Clausius inequality, demonstrate that
Fig. 2.2.
89