Carnot Cycle

Q. A Carnot engine whose sink is at $300$ $K$ has an efficiency of $40$%. By how much should the temperature of source be increased so as to increase its efficiency by $50$% of original efficiency?

1. 325 $K$
2. 250 $K$
3. 380 $K$
4. 275 $K$

Q. An ideal Carnot engine whose efficiency is 40% receives heat at 500 K. If its efficiency were 50%, then in take temperature for same exhaust temperature would be

1. 700 K
2. 800 K
3. 900 K
4. 600 K

Q. A Carnot engine has efficiency of $50\%$. If the temperature of sink is reduced by ${40}^{\circ }C$, its efficiency increases by $30\%$. The temperature of the source will be:

1. $366.7K$
2. $255.1K$
3. $266.7K$
4. $166.7K$

Q. The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is $-{20}^{\circ }C$, the temperature of the surroundings to which it rejects heat is:

1. ${11}^{\circ }C$
   
2. ${21}^{\circ }C$
   
3. ${31}^{\circ }C$
   
4. ${41}^{\circ }C$

Q.

Write an expression for calculating the efficiency of a machine.

Q. Two Carnot engines $A$ and $B$ are operated in succession. The first one, $A$ receives heat from a source at $T_1=800\text{K}$ and rejects to a sink at $T_2\text{K}$. The second engine $B$ receives heat rejected by the first engine and rejects to another sink at $T_3=300\text{K}$. Find the value of $T_2$ if
(i) the work outputs of the two engines are equal.
(ii) the efficiencies of the two engines are equal.

Q. The coefficient of performance of a Carnot refrigerator working between ${30}^{\circ }C$ and $0^{\circ }C$ is

1. 10
2. 9
3. 1
4. 0

Q. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by ${62}^{\circ }C$, the efficiency of the engine is doubled. The temperatures of the source and sink are

1. 99°C, 37°C
2. 80°C, 37°C
3. 95°C, 28°C
4. 90°C, 37°C

Q.

The efficiency of the Otto cycle is given by which of these expressions?Where r = compression ratio.

1. $1-\frac{1}{r^{\gamma -1}}$

2. $1-\frac{1}{{\gamma }^{r-1}}$

3. $\frac{1}{r}$

4. $\frac{1}{\gamma }$

Q.

Why is carnot cycle most efficient?

Q. The temperature of sink of Carnot engine is ${27}^{\circ }$C. Efficiency of engine is 25%. Then temperature of source is

1. 227^o C
2. 327^o C
3. 127^o C
4. 27^o C

Q.

A heat engine is involved with the exchange of heat of $1950J$, $-40J$, $+125J$ and $-QJ$, during one cycle achieving an efficiency of $50.0\%$. the value of $Q$ is:

1. $980J$

2. $640J$

3. $40J$

4. $400J$

Q.

What is the equivalent of 1 joule in calories?

Q.

How can we increase the efficiency of a heat engine?

Q.

A reversible heat engine converts one- fourth of the heat input into work. When the temperature of the sink is reduced by $52K$, its efficiency is doubled. The temperature in Kelvin of the source will be_______.

Q.

A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings. Specific heat of aluminium = 0.91 J g^–1 K^–1.

Q.

How do you increase Carnot efficiency?

Q. A Carnot engine whose source is at 400 K takes 200 cal of heat and rejects 150 cal to the sink. What is the temperature of the sink?

1. cannot say
2. 800 K
3. 400 K
4. 300 K

Q.

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$. The temperature of the hot reservoir of the first engine is ${\mathrm{T}}_1$ and the temperature of the cold reservoir of the second engine is ${\mathrm{T}}_2$. $\mathrm{T}$ is the temperature of the sink of first engine which is also the source for the second engine. How is $\mathrm{T}$ related to ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ if both the engines perform equal amount of work?

1. $\mathrm{T}=\frac{2{\mathrm{T}}_1{\mathrm{T}}_2}{({\mathrm{T}}_1+{\mathrm{T}}_2)}$

2. $\mathrm{T}=\frac{{\mathrm{T}}_1+{\mathrm{T}}_2}{2}$

3. $\mathrm{T}=0$

4. $\mathrm{T}=\sqrt{{\mathrm{T}}_1{\mathrm{T}}_2}$

Q. What is the temperature of source in Carnot cycle of 10% efficiency when heat exhausts at 270 K?

1. 400 K
2. 500 K
3. 600 K
4. 300 K

Q. A thermodynamic cycle with an ideal gas as working fluid is shown below.


If the specific heats of the working fluid are constant and the value of specific heat ratio $\gamma$ is $1.4$, the thermal efficiency $\left(\text{in}\%\right)$ of the cycle is

1. $21$
2. $42$
3. $2.1$
4. $0.21$

Q. A carnot engine having an efficiency of $\eta =\frac{1}{5}$ is used as a heat engine. Now it is used as a refrigerator. If work done by compressor is $40\text{J}$, the amount of energy delivered to surroundings is

1. $200\text{J}$
2. $160\text{J}$
3. $120\text{J}$
4. $50\text{J}$

Q. A Carnot engine whose sink is at $300K$ has an efficiency of $40\%$. By how much should the temperature of source be increased so as to increase its efficiency by $50\%$ of original efficiency?

1. $280K$
2. $275K$
3. $325K$
4. $250K$

Q.

A Carnot engine absorbs an amount Q of heat from a reservoir at an abosolute temperature T and rejects heat to a sink at a temperature of $\frac{T}{3}$. The amount of heat rejected is

1. Q / 4

2. Q / 3

3. Q / 2

4. 2Q / 3

Q.

What is the Industrial Unit of Power?

Q.

A Carnot's engine used first an ideal monoatomic gas then an ideal diatomic gas. If the source and sink temperature are ${411}^{\circ }C$ and ${69}^{\circ }C$respectively and the engine extracts 1000 J of heat in each cycle, then area enclosed by the PV diagram is

1. 100 J

2. 300 J

3. 500 J

4. 700 J

Q. The temperature inside and outside of the refrigerator is $260\text{K}$ and $315\text{K}$ respectively. Assuming that the refrigerator cycle is reversible, calculate the heat delivered to the surroundings for every joule of work done.

1. $5\text{J}$
2. $5.73\text{J}$
3. $6.19\text{J}$
4. $5\text{J}$

Q.

In one cycle of the engine, the net change in the entropy of both reservoirs (hot and cold together) is:

1. zero

2. greater than or equal to zero

3. less than zero

4. depends on the type of engine

Q. Temperature of source is ${330}^{\circ }C$. Temperature of sink is changed in order to increase the efficiency of engine from $\frac{1}{5}$ to $\frac{1}{4}$, by

1. $30K$
2. $303K$
3. $603K$
4. $60K$

Q.

Figure below represents a Carnot engine that works between temperatures $T_1$ 400 K and $T_2$ 150 K and drives aCarnot refrigerator that works between temperatures $T_3$ 325 K and $T_4$ 225 K.What is the ratio $\frac{Q3}{Q1}$?

1. 104/85

2. 104/95

3. 85/104

4. 95/104