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Chapter 12: Problem 68

Even Carnot engine cannot give \(100 \%\) efficiency because we cannot (A) prevent radiation. (B) find ideal sources. (C) reach absolute zero temperature. (D) eliminate friction.

Short Answer

Expert verified
The most accurate reason why even a Carnot engine cannot have 100% efficiency is because we cannot reach absolute zero temperature (option C). The efficiency of the Carnot engine depends on the difference between the high and low temperatures, and since reaching absolute zero is not possible, 100% efficiency cannot be achieved.

Step by step solution

01

Analyze the given options

Begin by analyzing the given options (A) to (D), focusing on which one is most related to the temperature aspect of the Carnot engine and will affect its efficiency the most: (A) Prevent radiation - Radiation can cause energy loss, which reduces the efficiency of the system. However, the Carnot engine is a theoretical model, assuming no energy loss. Thus, radiation is not the major factor here. (B) Find ideal sources - It is not easy to find ideal sources in reality, but in a theoretical model, idealized sources can be assumed. This reasoning does not directly relate to the efficiency limitation of the Carnot engine. (C) Reach absolute zero temperature - The efficiency of the Carnot engine depends on the difference between the high and low temperatures, where the lower temperature (T_low) can never equal absolute zero. Hence, this option seems to be a plausible candidate for our answer. (D) Eliminate friction - Friction can also cause energy loss and reduce the efficiency of the system. However, as stated before, the Carnot engine is a theoretical model, and it assumes zero friction. Thus, this aspect is not the main reason for the efficiency limitation.
02

Choose the correct option

After analyzing the given options, we can conclude that the option most related to the temperature aspect of the Carnot engine and its efficiency limitation is: (C) Reach absolute zero temperature The efficiency of the Carnot engine is given by: \( Eff = 1 - \frac{T_{low}}{T_{high}} \) If \(T_{low}\) reaches absolute zero (0 K), the efficiency would become 100%, but reaching absolute zero is not possible. Hence, even a Carnot engine cannot have 100% efficiency due to this reason.

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Most popular questions from this chapter

Two gases have same initial pressure, volume, and temperature. They expand to same final volume, one adiabatically and the other isothermally. (A) The final temperature is greater for isothermal process. (B) The final temperature is lesser for isothermal process. (C) The work done by the gas is greater for isothermal process. (D) The work done by the gas is greater for adiabatic process.

Three samples of the same gas \(A, B\), and \(C(\gamma=3 / 2)\) have initial equal volumes. Now the volume of each sample is doubled. The process is adiabatic for \(A\), isobaric for \(B\), and isothermal for \(C\). If the final pressures are equal for all three samples, the ratio of their initial pressures is (A) \(2 \sqrt{2}: 2: 1\) (B) \(2 \sqrt{2}: 1: 2\) (C) \(\sqrt{2}: 1: 2\) (D) \(2: 1: \sqrt{2}\)

A gas expands under constant pressure \(P\) from volume \(V_{1}\) to \(V_{2}\). The work done by the gas is (A) \(P\left(V_{2}-V_{1}\right)\) (B) \(P\left(V_{1}-V_{2}\right)\) (C) \(P\left(V_{1}^{\gamma}-V_{2}^{\gamma}\right)\) (D) \(\frac{P V_{1} V_{2}}{V_{2}-V_{1}}\)

One mole of an ideal gas is enclosed in a cylinder fitted with a frictionless piston and occupies a volume of \(1.5\) litre at a pressure of \(1.2 \mathrm{~atm} .\) It is subjected to a process given by equation \(T=\alpha V^{2}, \gamma\) (adiabatic constant) for the gas \(=1.5\). Choose the wrong statement. Given \(R \alpha=80 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{lit}^{-2}(R=\) gas constant and \(\alpha\) is constant) (A) The \(P-V\) diagram of the process is a straight line. (B) The work done by the gas in increasing the volume of the gas to 9 litre is \(3150 \mathrm{~J}\). (C) The change in the internal energy of the gas is \(12600 \mathrm{~J}\). (D) The heat supplied to the gas in the process is 1575 J.

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion, part of the cycle and the volume of the gas increases from \(\mathrm{V}\) to \(32 \mathrm{~V}\), the efficiency of the engine is [2010] (A) \(0.25\) (B) \(0.5\) (C) \(0.75\) (D) \(0.99\)
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