Second law; reversible and irreversible processes — practice questions

Question 1 · difficulty L2 · understanding

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

• A. low thermal conductivity and high electrical conductivity
• B. low thermal conductivity and low electrical conductivity
• C. high thermal conductivity and high electrical conductivity
• D. high thermal conductivity and low electrical conductivity

Question 2 · difficulty L2 · understanding

An engine operating between the boiling and freezing points of water will have A. efficiency more than 27%. B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures. C. efficiency equal to $$27 \%$$ D. efficiency less than $$27 \%$$ Choose the correct answer from the options given below:

• A. B and C only
• B. B and D only
• C. B, C and D only
• D. A and B only

Question 3 · difficulty L2 · understanding

Work done by a Carnot engine operating between temperatures $$127^{\circ} \mathrm{C}$$ and $$27^{\circ} \mathrm{C}$$ is $$2 \mathrm{~kJ}$$. The amount of heat transferred to the engine by the reservoir is :

• A. 8 kJ
• B. 2 kJ
• C. 4 kJ
• D. 2.67 kJ

Question 4 · difficulty L2 · understanding

A Carnot engine operating between two reservoirs has efficiency $$\frac{1}{3}$$. When the temperature of cold reservoir raised by x, its efficiency decreases to $$\frac{1}{6}$$. The value of x, if the temperature of hot reservoir is $$99^\circ$$C, will be :

• A. 66 K
• B. 62 K
• C. 16.5 K
• D. 33 K

Question 5 · difficulty L2 · understanding

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : Efficiency of a reversible heat engine will be highest at $-273^{\circ} \mathrm{C}$ temperature of cold reservoir. Reason R : The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta=\left(1-\frac{T_{2}}{T_{1}}\right)$ In the light of the above statements, choose the correct answer from the options given below

• A. Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
• B. Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
• C. A is false but $\mathbf{R}$ is true
• D. A is true but $\mathbf{R}$ is false

Question 6 · difficulty L2 · understanding

Let $$\eta_{1}$$ is the efficiency of an engine at $$T_{1}=447^{\circ} \mathrm{C}$$ and $$\mathrm{T}_{2}=147^{\circ} \mathrm{C}$$ while $$\eta_{2}$$ is the efficiency at $$\mathrm{T}_{1}=947^{\circ} \mathrm{C}$$ and $$\mathrm{T}_{2}=47^{\circ} \mathrm{C}$$ The ratio $$\frac{\eta_{1}}{\eta_{2}}$$ will be :

• A. 0.41
• B. 0.56
• C. 0.73
• D. 0.70

Question 7 · difficulty L2 · understanding

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

• A. 26.81%
• B. 37.81%
• C. 47.81%
• D. 57.81%

Question 8 · difficulty L2 · understanding

A Carnot engine whose heat sinks at 27$$^\circ$$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. Increases by 18$$^\circ$$C
• B. Increases by 200$$^\circ$$C
• C. Increases by 120$$^\circ$$C
• D. Increases by 73$$^\circ$$C

Question 9 · difficulty L2 · understanding

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S 1 and that of the other part is S 2 . Given that S 1 > S 2 . If the piston is removed then the total entropy of the system will be :

• A. S 1 $$-$$ S 2
• B. $${{{S_1}} \over {{S_2}}}$$
• C. S 1 $$\times$$ S 2
• D. S 1 + S 2

Question 10 · difficulty L2 · understanding

A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

• A. 2400 J
• B. 1600 J
• C. 1800 J
• D. 3200 J