# Find the total work w done by the gas after it completes a single carnot cycle.

A) Which of the following statements are
true? A) Check all that apply

For the gas to do positive work, the cycle must be traversed in
a clockwise manner.

Positive heat is added to the gas as it proceeds from state C
to state D.

The net work done by the gas is proportional to the area inside
the closed curve.

The heat transferred as the gas proceeds from state B to state C
is greater than the heat transferred as the gas proceeds from state
D to state A.

For the gas to do positive work, the cycle must be traversed in
a clockwise manner.

Positive heat is added to the gas as it proceeds from state C
to state D.

The net work done by the gas is proportional to the area inside
the closed curve.

The heat transferred as the gas proceeds from state B to state C
is greater than the heat transferred as the gas proceeds from state
D to state A.

For the gas to do positive work, the cycle must be traversed in
a clockwise manner.
For the gas to do positive work, the cycle must be traversed in
a clockwise manner.
Positive heat is added to the gas as it proceeds from state C
to state D.
Positive heat is added to the gas as it proceeds from state C
to state D.
The net work done by the gas is proportional to the area inside
the closed curve.
The net work done by the gas is proportional to the area inside
the closed curve.

The heat transferred as the gas proceeds from state B to state C
is greater than the heat transferred as the gas proceeds from state
D to state A.

The heat transferred as the gas proceeds from state B to state C
is greater than the heat transferred as the gas proceeds from state
D to state A.
B) Find the total work W done by the
gas after it completes a single Carnot cycle. B) W Express the work in terms of any or all of the quantities
|Qh|, Th,
|Qc|, and
Tc Qh Q Th T Qc Q Tc T ​C) Suppose there are n moles of the
ideal gas, and the volumes of the gas in states A and B are,
respectively, VA and VB. Find Qh, the
heat absorbed by the gas as it expands from state A to state B.
Note that in this part, we are not looking for
|Qh|. ​C) n V V Q not Q Express the heat absorbed by the gas in terms of
n, VA,
VB, the temperature of the hot reservoir,
Th, and the gas constant n n VA V VB V Th T D) The volume of the gas in state C is
VC, and its volume in state D is VD. Find
Qc, the magnitude of the heat that flows out of the gas as
it proceeds from state C to state D. Express your answer in terms
of n, VC,
VD, Tc (the
temperature of the cold reservoir), and
R D) V V Q n n VC V VD V Tc T R R E) Now, by considering the adiabatic processes
(from B to C and from D to A), find the ratio
VC/VD in terms of VA and
VB. E) V V V V F) Using your expressions for |Qh| and
|Qc| (found in Parts C and D), and your result from Part
E, find a simplified expression for
|Qc|/|Qh|. F) Q Q simplified Q Q No volume variables should appear in your expression, nor should
any constants (e.g., n or
R) n n R) R) ​G) The efficiency of any engine is,
by definition, e=W/Qh. Carnot proved
that no engine can have an efficiency greater than that of a Carnot
engine. Find the efficiency eCarnot of a Carnot
engine. ​G) ​ e W Q e Express the efficiency in terms of Th
and Tc. Th T Tc T Isothermal expansion Ti Adiabatic compression Adiabatic expansion Isothermal compression Te C

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If capacitance of air filled capacitor is C and voltage across it is then charge on each capacitor plate is Q = CV CV = Q = 71°C When a dielectric slab of dielectric constant k is inserted the new capacitance becomes k times Cnew = kc Since capacitor is still connected to the same battery therefore voltage across the capacitor is still same. Now new charge on the capacitor plates is Qnew = CnewV KCV = 71 + 307 = 378 C Now kCV CV – 3784C 714C 378 k= 71 k = 5.324 Therefore dielectric constant of the slab is 5.324
A) # For the gas to do positive work, the cycle must be traversed in a clockwise manner. The statement is true For a heat engine cycle must be traversed in a clockwise manner and for refrigeration cycle must be traversed in counterclockwise manner. # Positive heat is added to the gas as it proceeds from state C to state D. This statement is false From first law of thermodynamics QcD = WCD+ AUCD Since temperature is constant in CD process therefore change in internal energy is zero in this process therefore heat added is equal to the work done by the gas in this process CD Since in process CD volume is decreasing (isothermal compression ) therefore work done is negative hence heat added in this process is negative. # The net work done by the gas is proportional to the area inside the closed curve. In a closed PV cycled area enclosed represents the work done in this cycle. Therefore this statement is true # The heat transferred as the gas proceeds from state B to state C is greater than the heat transferred as the gas proceeds from state D to state A. This statement is false as the process BC and DA is adiabatic and in adiabatic process no heat exchange takes place.
B ) Heat added from the source does some work and rest of the heat is rejected to sink therefore form energy conservation |01| = = W+ 100 Therefore the total work done by the gas after it completes a single Carnot cycle is w = 10,1 – 1901 C) the heat absorbed by the gas as it expands from state A to state B. On = nRT,In rum) D) the magnitude of the heat that flows out of the gas as it proceeds from state C to state D Qc = nRT In E) In adiabatic processes (from B to C and from D to A) 7,7%;’ =TV?! 1,1%” = TV: Divide both the equation
VC VD the ratio VC/VD in terms of VA & VB is VC VD F) simplifying expression for Qc/I Qh | |0c| = nRT in |9,1| = nRT, in nRT In OC |26| nRT,In Since VA V. VD V So – nRT In -(0) |9c| |04| nRT,In TO ala
G) the efficiency of a Carnot engine is W e Qh Qn-Qc Oh e=1 – Qc en TC e- e=1- Th

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