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Chapter 8: Problem 1106

One mole of a monoatomic gas is heat at a constant pressure of 1 atmosphere from \(0 \mathrm{k}\) to \(100 \mathrm{k}\). If the gas constant $\mathrm{R}=8.32 \mathrm{~J} / \mathrm{mol} \mathrm{k}$ the change in internal energy of the gas is approximate ? (A) \(23 \mathrm{~J}\) (B) \(1.25 \times 10^{3} \mathrm{~J}\) (C) \(8.67 \times 10^{3} \mathrm{~J}\) (D) \(46 \mathrm{~J}\)

Short Answer

Expert verified
The change in internal energy of the monoatomic gas is approximately \(1.25 \times 10^{3} \mathrm{~J}\).

Step by step solution

01

Find the value of Cv for monoatomic gas

Monoatomic gases have a constant volume heat capacity (Cv) equal to (3/2)R, where R is the gas constant (Given: R = 8.32 J/mol K). So, let's find the value of Cv: Cv = (3/2) * R Cv = (3/2) * 8.32 J/mol K Cv ≈ 12.48 J/mol K
02

Calculate the change of internal energy using the formula for ΔU (Cv)

Now, from the given initial and final temperatures, we can determine the change in temperature (ΔT). Then, we will use the formula for the change in internal energy ΔU with the values of n, Cv, and ΔT that we have. ΔT = T(final) - T(initial) ΔT = 100 K - 0 K ΔT = 100 K ΔU = nCvΔT ΔU = (1 mol) (12.48 J/mol K) (100 K) ΔU ≈ 1248 J Since the change in internal energy is approximately equal to 1248 J, the correct answer is: (B) 1.25 x 10^3 J

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Most popular questions from this chapter

For an isothermal expansion of a Perfect gas, the value of $(\Delta \mathrm{P} / \mathrm{P})$ is equal to (A) \(-\gamma^{(1 / 2)}\\{(\Delta \mathrm{V}) / \mathrm{V}\\}\) (B) \(-\gamma\\{(\Delta \mathrm{V}) / \mathrm{V}\\}\) (C) \(-\gamma^{2}\\{(\Delta \mathrm{V}) / \mathrm{V}\\}\) \((\mathrm{D})-(\Delta \mathrm{V} / \mathrm{V})\)

\(1 \mathrm{~mm}^{3}\) Of a gas is compressed at 1 atmospheric pressure and temperature \(27^{\circ} \mathrm{C}\) to \(627^{\circ} \mathrm{C}\) What is the final pressure under adiabatic condition. \(\mathrm{r}=1.5\) (A) \(80 \times 10^{5}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(36 \times 10^{5}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(56 \times 10^{5}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(27 \times 10^{5}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

A Carnot engine having a efficiency of \(\mathrm{n}=(1 / 10)\) as heat engine is used as a refrigerators. if the work done on the system is \(10 \mathrm{~J}\). What is the amount of energy absorbed from the reservoir at lowest temperature ! (A) \(1 \mathrm{~J}\) (B) \(90 \mathrm{~J}\) (C) \(99 \mathrm{~J}\) (D) \(100 \mathrm{~J}\)

\(\mathrm{Cp}\) and Cv denote the specific heat of oxygen per unit mass at constant Pressure and volume respectively, then (A) \(\mathrm{cp}-\mathrm{cv}=(\mathrm{R} / 16)\) (B) \(\mathrm{Cp}-\mathrm{Cv}=\mathrm{R}\) (C) \(\mathrm{Cp}-\mathrm{Cv}=32 \mathrm{R}\) (D) \(\mathrm{Cp}-\mathrm{Cv}=(\mathrm{R} / 32)\)

A monoatomic gas is used in a Carnot engine as the working substance, If during the adiabatic expansion part of the cycle the volume of the gas increases from \(\mathrm{V}\) to \(8 \mathrm{~V}_{1}\) the efficiency of the engine is.. (A) \(60 \%\) (B) \(50 \%\) (C) \(75 \%\) (D) \(25 \%\)
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