Carnot cycle

As shown in the figure, five Carnot engines, each with efficiency $\eta$ and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider $Q_0$ to be the amount of heat absorbed per cycle by the first engine and $W$ as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be $\eta_{\text{net}}=\dfrac W{Q_0}=\dfrac{211}{243}$. The value of $\eta$ is:

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10. The hot reservoir of the heat pump is at a temperature of 300 K. Which of the following statements is/are correct:

A Carnot engine whose heat sinks at 27°C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency ?

A Carnot engine takes 5000 kcal of heat from a reservoir at 727°C and gives heat to a sink at 127°C. The work done by the engine is

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is ______ K.

In a carnot engine, the temperature of reservoir is 527°C and that of sink is 200 K. If the workdone by the engine when it transfers heat from reservior to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is ______ $\times10^6$ J.

300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is 227°C, then the temperature of sink will be ______ °C.

Let $\eta_1$ is the efficiency of an engine at $T_1=447$°C and $T_2=147$°C while $\eta_2$ is the efficiency at $T_1=947$°C and $T_2=47$°C. The ratio $\dfrac{\eta_1}{\eta_2}$ will be :

Read the following statements :

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies P and Q having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by P and Q are in the ratio 1:1.15.

C. A Carnot Engine working between 100K and 400K has an efficiency of 75%.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

In 1$^{\text{st}}$ case, Carnot engine operates between temperatures 300 K and 100 K. In 2$^{\text{nd}}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2$^{\text{nd}}$ case) will be :

A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be :

A Carnot engine is operating between the two reservoirs of temperature 227 °C and 127 °C respectively. If the engine performs $1.04\times10^5$ J work per cycle. Then, the heat absorbed from hot reservoir per cycle will be :

A Carnot freezer takes heat from water at 0°C inside it and rejects it to the room at a temperature of 27°C. The latent heat of ice is $336\times10^3$ J kg$^{-1}$. If 5 kg of water at 0°C is converted into ice at 0°C by the freezer, then the energy consumed by the freezer is close to :

A Carnot engine absorbs 1000 J of heat energy from a reservoir at 127°C and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be :