B.3 Gas laws

Since the cylinder is rigid (constant volume) and sealed (constant $n$), Gay-Lussac's Law applies: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$. Convert temperatures: $T_1=27+273=300$ K, $T_2=127+273=400$ K.

Rearranging: $P_2=P_1\times \frac{T_2}{T_1}=(1.5\times 10^5)\times \frac{400}{300}$.

$P_2=1.5\times 10^5\times \frac{4}{3}=2.0\times 10^5\text{ Pa}$

The new pressure is $2.0\times 10^5$ Pa. This makes sense: raising temperature increases molecular speed, so collisions with walls are harder and more frequent, increasing pressure.

The question asks for pressure after heating at constant volume. The ratio $T_2/T_1=400/300=4/3$, so pressure must increase by a factor of $4/3$.

This is less than the initial pressure. Heating a gas at constant volume increases pressure, so this is impossible — eliminate it.

This equals the initial pressure, implying no change. Since temperature has increased, pressure must increase — eliminate it.

This would require a factor of about 3.7 increase. This would result from incorrectly using Celsius temperatures ($127/27\approx 4.7$) — a common error. Eliminate it.

$2.0\times 10^5$ Pa corresponds to multiplying by $400/300=4/3$, which is the correct ratio of Kelvin temperatures. This is the correct answer.

The ideal gas model requires: (1) negligible molecular volume compared to the container, (2) no intermolecular forces except during collisions, (3) perfectly elastic collisions, and (4) continuous random motion.

Option A states 'no intermolecular forces except during collisions' — this matches assumption (2) exactly.

Option A is a core assumption of the ideal gas model. All other options contradict the model's assumptions.

The question requires identifying a genuine assumption of the ideal gas model from four statements.

In a real gas (and in kinetic theory), molecules have a distribution of speeds (Maxwell-Boltzmann distribution). Identical speeds is not an assumption — eliminate this.

The ideal gas model requires perfectly elastic collisions so that kinetic energy is conserved. Perfectly inelastic collisions would cause the gas to lose energy and slow down — eliminate this.

The model assumes molecules have negligible volume compared to the container. If their volume were comparable, the gas would deviate significantly from ideal behaviour — eliminate this.

'No intermolecular forces except during collisions' is a genuine and necessary assumption of the ideal gas model. This is the correct answer.