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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

A monoatomic ideal gas, intially at temperature \(1_{1}\) is enclosed in a cylinders fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \(\mathrm{T}_{2}\) by releasing the piston suddenly If \(\mathrm{L}_{1}\) and \(\mathrm{L}_{2}\) the lengths of the gas column before and after expansion respectively, then then \(\left(\mathrm{T}_{1} / \mathrm{T}_{2}\right)\) is given by (A) \(\left\\{\mathrm{L}_{1} / \mathrm{L}_{2}\right\\}^{(2 / 3)}\) (B) \(\left\\{\mathrm{L}_{2} / \mathrm{L}_{1}\right\\}^{(2 / 3)}\) (C) \(\left\\{\mathrm{L}_{1} / \mathrm{L}_{2}\right\\}\) (D) \(\left\\{\mathrm{L}_{2} / \mathrm{L}_{1}\right\\}\)

At Which temperature the density of water is maximum? (A) \(4^{\circ} \mathrm{F}\) (B) \(42^{\circ} \mathrm{F}\) (C) \(32^{\circ} \mathrm{F}\) (D) \(39.2^{\circ} \mathrm{F}\)

In a container of negligible heat capacity, \(200 \mathrm{~g}\) ice at \(0^{\circ} \mathrm{C}\) and \(100 \mathrm{~g}\) steam at \(100^{\circ} \mathrm{C}\) are added to \(200 \mathrm{~g}\) of water that has temperature $55^{\circ} \mathrm{C}$. Assume no heat is lost to the surroundings and the pressure in the container is constant \(1 \mathrm{~atm} .\) Amount of the Sm left in the system, is equal to (A) \(16.7 \mathrm{~g}\) (B) \(8.4 \mathrm{~g}\) (C) \(12 \mathrm{~g}\) (D) \(0 \mathrm{~g}\) Copyright () StemEZ.com. All rights reserved.

The change in internal energy, when a gas is cooled from $927^{\circ} \mathrm{C}\( to \)27^{\circ} \mathrm{C}$ (A) \(200 \%\) (B) \(100 \%\) (C) \(300 \%\) (D) \(400 \%\)

Two cylinders \(\mathrm{A}\) and \(\mathrm{B}\) fitted with piston contain equal amounts of an ideal diatomic gas at \(300 \mathrm{k}\). The piston of \(\mathrm{A}\) is free to move, While that of \(B\) is held fixed. The same amount of heat is given to the gas in each cylinders. If the rise in temperature of the gas in \(\mathrm{A}\) is \(30 \mathrm{~K}\), then the rise in temperature of the gas in \(\mathrm{B}\) is. (A) \(30 \mathrm{~K}\) (B) \(42 \mathrm{~K}\) (C) \(18 \mathrm{~K}\) (D) \(50 \mathrm{~K}\)
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