Discussion
Equation of state for dry atmosphere is given by :
Answer: A
The equation of state is \(p = \frac{\rho R}{m} T\).
Dry air behaves as an ideal gas. Writing the ideal gas law per unit volume, with \(\rho\) the density, \(m\) the mean molecular mass of dry air (about 28.97 g/mol) and \(R\) the universal gas constant:
\[ \begin{aligned} pV &= nRT = \frac{M}{m} RT \\ p &= \frac{\rho R}{m} T = \rho R_{d} T \end{aligned} \]
Here \(R_{d} = R/m\), about 287 J/(kg K), is the gas constant for dry air. Options with \(\alpha\) use the specific volume \(\alpha = 1/\rho\); the correct form with it would be \(p\alpha = R_{d}T\), so \(p = \alpha RT\) and \(p\alpha = R/m\) (which drops the temperature) are both wrong, as is \(p = \frac{\alpha R}{m}T\).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development