Exams › JEE Main › Physics

This item contains two statements. From the four alternatives that follow, select the one that most accurately describes the statements. Statement 1: An inventor says they have made an engine with 30% efficiency while working between the freezing point and the boiling point of water. Such an engine cannot exist. Statement 2: For the same pair of temperatures, no actual engine can have an efficiency greater than that of a Carnot engine.

1. Statement 1 is correct, Statement 2 is correct, but Statement 2 does not explain Statement 1.
2. Statement 1 is correct, Statement 2 is incorrect.
3. Statement 1 is incorrect, Statement 2 is correct.
4. Statement 1 is correct, Statement 2 is correct, and Statement 2 correctly explains Statement 1.

Correct answer: Statement 1 is correct, Statement 2 is correct, and Statement 2 correctly explains Statement 1.

Solution

Both statements are accurate; the first asserts that an engine with 30% efficiency operating between the specified temperatures is impossible, while the second explains that no engine can exceed the efficiency of a Carnot engine under those conditions, thus validating the first statement.

Related JEE Main Physics questions

• For the equation \((P + a/\sqrt{2})(V - b) = \text{constant}\), what is the dimensional unit of the constant \(a\)?
• A refrigerator operates between \(4^\circ\text{C}\) and \(30^\circ\text{C}\). To maintain its interior at a steady temperature, it must extract 600 calories of heat each second. If 1 calorie = 4.2 joule, the power needed is:
• A diatomic gas with adiabatic index \(\gamma = 1.4\) is initially at a pressure of 2 atm. It is compressed adiabatically until its temperature increases from \(27^\circ\text{C}\) to \(927^\circ\text{C}\). What is the final pressure of the gas?
• A Carnot engine operates with a diatomic ideal gas as its working fluid. During the adiabatic expansion stage, the gas volume rises from \(V\) to \(32V\). What is the efficiency of the engine?
• A spherical cavity of radius $R$ contains black-body radiation at temperature $T$. Treat the radiation as a photon gas with energy density $u=U/V$ proportional to $T^4$ and pressure $p=\frac{1}{3}(U/V)$. If the cavity expands adiabatically, how are $T$ and $R$ related?
• A metal has low-temperature specific heat capacity given by $C=32\left(\frac{T}{400}\right)^3\,\text{J K}^{-1}\text{kg}^{-1}$. If a 100 g container made of this metal is to be cooled from 20 K down to 4 K using a special refrigerator working at room temperature ($27^\circ$C), the work needed for the cooling process is

⚔️ Practice JEE Main Physics free + battle 1v1 →