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Chapter 8: Problem 1149

An adiabatic Bulk modulus of an ideal gas at Pressure \(\mathrm{P}\) is (A) \(\gamma \mathrm{P}\) (B) \((\mathrm{p} / \gamma)\) (C) \(\mathrm{P}\) (D) \((\mathrm{p} / 2)\)

Short Answer

Expert verified
The short answer is: The adiabatic Bulk modulus of an ideal gas at pressure \(P\) is (A) \(\gamma P\), where \(\gamma\) is the adiabatic index (heat capacity ratio).

Step by step solution

01

Write down the adiabatic bulk modulus formula

The formula for the adiabatic bulk modulus of an ideal gas (\(B_{\text{adiabatic}}\)) in terms of pressure (\(P\)) and adiabatic index (\(\gamma\)) is: \[B_{\text{adiabatic}} = \gamma P\]
02

Compare the formula with the given options

We will now compare the formula \(B_{\text{adiabatic}} = \gamma P\) with the given options to determine which one is correct: (A) \(\gamma P\) (B) \(\dfrac{P}{\gamma}\) (C) \(P\) (D) \(\dfrac{P}{2}\)
03

Select the correct option

By comparing the formula \(B_{\text{adiabatic}} = \gamma P\) with the given options, we see that the correct option is (A) \(\gamma P\).

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Most popular questions from this chapter

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) \(50 \mathrm{~K}\)

What is an adiabatic Bulk modulus of hydrogen gas at NTP? (A) \(1.4\left(\mathrm{~N} / \mathrm{M}^{2}\right)\) (B) \(1.4 \times 10^{5}\left(\mathrm{~N} / \mathrm{M}^{2}\right)\) (C) \(1 \times 10^{-8}\left(\mathrm{~N} / \mathrm{M}^{2}\right)\) (D) \(1 \times 10^{5}\left(\mathrm{~N} / \mathrm{M}^{2}\right)\)

70 calorie of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from \(30^{\circ} \mathrm{C}\) to $35^{\circ} \mathrm{C}$ The amount of heat required to raise the temperature of the same gas through the same range at constant volume is $\ldots \ldots \ldots \ldots \ldots .$ calorie. (A) 50 (B) 30 (C) 70 (D) 90

In an isothermal reversible expansion, if the volume of \(96 \mathrm{~J}\) of oxygen at \(27^{\circ} \mathrm{C}\) is increased from 70 liter to 140 liter, then the work done by the gas will be (A) \(300 \mathrm{R} \log _{\mathrm{e}}^{(2)}\) (B) \(81 \mathrm{R} \log _{\mathrm{e}}^{(2)}\) (C) \(2.3 \times 900 \mathrm{R} \log _{10} 2\) (D) \(100 \mathrm{R} \log _{10}^{(2)}\)

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) \(39.2^{\circ} \mathrm{F}\)
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