Henry's law is expressed as follows: \[ C = k_H P \] Definitions:
- \( C \) represents the solubility of the gas in mol dm\(^{-3}\),
- \( k_H \) is Henry's constant, here \( 0.159 \, \text{mol dm}^{-3} \text{ bar}^{-1} \),
- \( P \) stands for the partial pressure of the gas, \( 0.164 \, \text{bar} \).
Calculating the solubility: \[ C = 0.159 \times 0.164 = 0.0261 \, \text{mol dm}^{-3} \]
The ratio of the fundamental vibrational frequencies \( \left( \nu_{^{13}C^{16}O} / \nu_{^{12}C^{16}O} \right) \) of two diatomic molecules \( ^{13}C^{16}O \) and \( ^{12}C^{16}O \), considering their force constants to be the same, is ___________ (rounded off to two decimal places).}
A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]