Pressure-temperature Law

At constant volume the pressure of a fixed amount of ideal gas is directly proportional to its absolute temperature, a result known as Gay-Lussac's law: $\frac{P_1}{T_1}=\frac{P_2}{T_2}$. This follows from $PV=nRT$ with $V$ and $n$ held fixed, and microscopically it reflects that hotter molecules strike the walls both harder and more frequently. Solving for the new pressure, $P_2=P_1\frac{T_2}{T_1}=2.0\times 10^5\times \frac{450}{300}=3.0\times 10^5$ Pa. The temperatures must be expressed in kelvin for the proportionality to hold correctly. The value $1.33\times 10^5$ Pa inverts the temperature ratio. The value $4.5\times 10^5$ Pa mistakenly multiplies by an incorrect ratio arising from a celsius-to-kelvin confusion. The value $2.5\times 10^5$ Pa wrongly adds a fixed increment rather than scaling proportionally. This is the NCERT pressure–temperature law for an isochoric process, derived directly from the ideal gas equation and important for understanding why sealed containers can burst when heated near a flame and why pressure cookers and aerosol cans carry temperature warnings. As a plausibility check, raising the temperature by 50 % (from 300 K to 450 K) should raise the pressure by the same 50 %, taking $2.0\times 10^5$ Pa to $3.0\times 10^5$ Pa, exactly matching our computed result.