Gases and Gas Laws

Density is mass divided by volume. When the volume is reduced to half while the mass remains constant, the density must double. The initial density of 1 kg/m³ becomes 2 kg/m³ after compression.

The bandwidth of a narrow band communication channel is 64 Kbps. This is a standard telecommunications specification - 64 Kbps (kilobits per second) is the bandwidth of a single digital voice channel, commonly used in ISDN and other telephony standards. The option '64KBps' would be incorrect as it refers to kilobytes.

The flame velocity of a methane-air mixture is approximately 40 cm/s. This is a characteristic property of methane combustion in air at standard conditions. Option A (10 cm/s) is too slow, while options C and D (1 m/s and 4 m/s) are an order of magnitude too fast.

The lower flammability limit (LFL) of hydrogen in air is 4% by volume. Below this concentration, the mixture is too lean to burn. Options A (0.4%), B (3%), and D (8%) are incorrect - 0.4% is too low, 3% is close but not the standard value, and 8% approaches the upper flammability limit.

350 PPM (parts per million) is considered the safe upper limit for CO2 concentration in the atmosphere to maintain climate stability. Beyond this level, risks of dangerous climate change increase significantly. The question reflects climate science concerns from the 2000s when this target was actively discussed. Current levels exceed 400 PPM.

This is a myth. While gas compression occurs at depth due to increased water pressure, the gas in the digestive tract does compress but does not prevent flatulence. In fact, some divers report increased gas due to pressure changes affecting digestion. At depth, compressed gas would actually be smaller in volume than at the surface.

GM sets calibration to 5mg/l. Worst passing value would be 5 + 10% of 5 = 5.5mg/l (at the upper edge of passing). Best failing value would be just above 5.5mg/l. But wait, the question mentions the Authority sets 10mg/l as permissible. Re-reading: if calibration is 5mg/l, and we need to find worst passing and best failing values relative to the calibration standard... With 10% tolerance: passing range is 4.5-5.5mg/l. Worst passing = 5.5mg/l. But that's not in the options. Let me reconsider... Ah, maybe the question is asking about values relative to the Authority's 10mg/l limit? If GM sets 5mg/l internally, and Authority allows 10mg/l, then worst passing at Authority level could be 9mg/l (still under 10), and best failing could be 11-12mg/l (above 10). The option shows 9, 12 which means: 9mg/l passes (under 10mg/l Authority limit), 12mg/l fails (above 10mg/l). This interpretation makes sense.

P_o = (1/3)(Nm/V) v² _rms (Here m = mass of each molecule, V = volume of the gas) Now , m’ = (1/2)m V^’ _rms = 2 v _rms P’ = (1/3)(Nm/2V)4 v² _rms      = 2 x (1/3)(Nm/V) v² _rms = 2 P_o

= 389 m/s

Pressure of the gas P = (1/3)(mN/V)v² _rms Here  V =10^-3m³ N = 3 x 10²² m = 5.3 x 10^-26 kg v _rms = 400 m/s ∴ P = (1/3){ 5.3 x 10^-26 x 3 x 10²² (400)²}/10^-3        = 8.48 x 10⁴ N/m²

Volume = mass / density = 7.8 g / 1.3 g/L = 6 L. This is a straightforward density calculation rearranged to find volume.

V = ?,  W = 7.0 gramT = 27^o C = 27+ 273 = 300^o KR = 0.082, Molecular wt. M = 28. According to ideal gas equation PV = w/M x R x T                                         V = (w x R x T)/(M x P) Substituting the values in this eq.                                              V = (5 x 760 x 0.082 x 300)/(28 x 750)                                                  = 4.451 litres.

Pressure is directly proportional to moles of gases.  4 grams of He = 1 mole of He gas (weight/molar weight); highest among all. Molecular weight of Helium gas is 4.

Total pressure = 5 atm. By Dalton's Law of partial pressure: P_{0xygen =} (5)*(0.2) = 1 atm. From Henry's Law:P_Oxygen = K_H * x1 = 2 * (n/n+10)Solving, n = 10