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Chapter 10: Problem 42

The internal energy \(U\) is a unique function of any state because change in \(U\) (A) does not depend upon path. (B) depends upon path. (C) corresponds to an adiabatic process. (D) corresponds to an isothermal process.

Short Answer

Expert verified
The internal energy U is a unique function of any state because it is a state function and change in U (A) does not depend upon the path.

Step by step solution

01

Understanding Internal Energy

Internal energy (U) is the total energy contained in a system, representing the sum of kinetic and potential energies of its particles. In thermodynamics, internal energy is a state function, meaning it depends only on the current state of the system and not on the path taken to reach that state.
02

Evaluating Statement (A)

(A) does not depend upon the path. This statement is true for internal energy. As a state function, internal energy does not rely on the path taken for the system to reach its current state. Instead, it depends solely on the current state variables(e.g., temperature, pressure, volume). This characteristic is a factor that contributes to internal energy being a unique function of any state.
03

Evaluating Statement (B)

(B) depends upon the path. This statement is false for internal energy. As we established in Statement (A), internal energy is a state function and does not rely on the path taken to reach the current state.
04

Evaluating Statement (C)

(C) corresponds to an adiabatic process. This statement is not directly related to the uniqueness of internal energy as a state function. An adiabatic process is one where there is no exchange of heat between the system and its surroundings. Although the internal energy will change during an adiabatic process, this does not make it a unique function of any state.
05

Evaluating Statement (D)

(D) corresponds to an isothermal process. This statement is also not directly related to the uniqueness of internal energy as a state function. An isothermal process is one where the temperature of the system remains constant. In this case, the internal energy may or may not change, but this does not make it a unique function of any state. After evaluating all statements, we can conclude that:
06

Final Conclusion

The internal energy U is a unique function of any state because change in U (A) does not depend upon the path.

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Most popular questions from this chapter

Heat required to melt \(1 \mathrm{gm}\) of ice is \(80 \mathrm{cal}\). A man melts \(60 \mathrm{gm}\) of ice by chewing it in 1 minute. Power supplied by the man to melt ice is (A) \(4800 \mathrm{~W}\) (B) \(336 \mathrm{~W}\) (C) \(80 \mathrm{~W}\) (D) \(0.75 \mathrm{~W}\)

\(10 \mathrm{gm}\) of ice at \(0^{\circ} \mathrm{C}\) is mixed with \(5 \mathrm{gm}\) of steam at \(100^{\circ} \mathrm{C}\). If latent heat of fusion of ice is \(80 \mathrm{cal} / \mathrm{gm}\) and latent heat of vaporization is \(540 \mathrm{cal} / \mathrm{gm}\). Then at thermal equilibrium (A) temperature of mixture is \(0^{\circ} \mathrm{C}\). (B) temperature of mixture is \(100^{\circ} \mathrm{C}\). (C) mixture contains \(13.33 \mathrm{gm}\) of water and \(1.67 \mathrm{gm}\) of steam. (D) mixture contains \(5.3 \mathrm{gm}\) of ice and \(9.7 \mathrm{gm}\) of water.

Cooking gas containers are loaded on to a truck moving with uniform speed. The temperature of the gas molecules inside the containers will (A) increase. (B) decrease. (C) remain same. (D) decrease for some, whereas increase for others.

An aluminium sphere of \(20 \mathrm{~cm}\) diameter is heated from \(0^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). Its volume changes by (given that the coefficient of linear expansion for aluminium \(\left.\alpha_{A l}=23 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) (A) \(28.9 \mathrm{cc}\) (B) \(2.89 \mathrm{cc}\) (C) \(9.28 \mathrm{cc}\) (D) \(49.8 \mathrm{cc}\)

A long metallic bar is carrying heat from one end to the other under steady state. The variation of temperature \(\theta\) along the length \(x\) of the bar from its hot end is best described by which of the following.
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