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Chapter 8: Problem 1150

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) \(1 \times 10^{5}\left(\mathrm{~N} / \mathrm{M}^{2}\right)\)

Short Answer

Expert verified
The adiabatic bulk modulus of hydrogen gas at NTP is approximately \(1 \times 10^5 \mathrm{~N} / \mathrm{M}^{2}\).

Step by step solution

01

Find the adiabatic index

The adiabatic index \(\gamma\) is the ratio of specific heat capacities, for diatomic gases like hydrogen, it is approximately \(\gamma = 1.4\). Keep this value for further calculations.
02

Find the pressure at NTP

Normal Temperature and Pressure (NTP) conditions, the pressure of the gas is 1 atm which is equivalent to \(1.013 \times 10^5 \mathrm{~N} / \mathrm{M}^{2}\).
03

Calculate the adiabatic bulk modulus

Now, we will calculate the adiabatic bulk modulus using the formula \( B_A = \gamma p \), where \(\gamma = 1.4\) and \(p = 1.013 \times 10^5 \mathrm{~N} / \mathrm{M}^{2}\). \(B_A = 1.4 \times (1.013 \times 10^5 \mathrm{~N} / \mathrm{M}^{2})\)
04

Compute the answer and compare with choices

Calculate the product and compare it with the given choices: \(B_A = 1.4 \times 1.013 \times 10^5 \mathrm{~N} / \mathrm{M}^{2} = 1.4182 \times 10^5 \mathrm{~N} / \mathrm{M}^{2}\) The closest answer to our calculation is (D) approximated to \(1 \times 10^5 \mathrm{~N} / \mathrm{M}^{2}\). Therefore, the adiabatic bulk modulus of hydrogen gas at NTP is approximately \(1 \times 10^5 \mathrm{~N} / \mathrm{M}^{2}\).

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