A bulb of three litre capacity filled with air is heated from \(27^{\circ} \mathrm{C}\) to \(t^{\circ} \mathrm{C}\). The air thus, expelled measured \(1.45\) litre at \(17^{\circ} \mathrm{C}\). Considering the pressure to be 1 atm throughout the experiment and ignoring the expansion of bulb, calculate \(t\).

Gas law calculations are essential components of chemistry, especially when dealing with the behavior of gases under various temperature and pressure conditions. One of the fundamental laws for these calculations is Charles's Law, which shows the direct relationship between a gas's volume and temperature when pressure is held constant. The formula is expressed as \( V_1/T_1 = V_2/T_2 \) where \( V \) represents volume and \( T \) represents temperature in Kelvin. It's important for students to understand that before applying this law, all temperature measurements must be converted to Kelvin, as this scale provides an absolute referencing for temperature measurements essential for the calculations.

Additionally, to solve problems using Charles's Law, the proper rearrangement of the law's formula is crucial to isolate the variable one seeks to find. In the context of the given exercise, once the initial and final volumes and temperatures are known, the formula can be manipulated to solve for the final temperature after thermal expansion.

Temperature conversion between Celsius and Kelvin scales is a fundamental process in solving gas law problems. The Kelvin scale is an absolute temperature scale where 0 K corresponds to absolute zero, the point at which all molecular motion stops. To convert from Celsius to Kelvin, one simply adds 273.15 (usually approximated as 273 for simplicity in most chemistry problems) to the Celsius temperature. Conversely, to convert from Kelvin back to Celsius, one subtracts 273 from the Kelvin temperature.

It is crucial to perform these conversions accurately because gas law formulas require temperatures in Kelvin. This ensures that the thermal expansion of gases is accurately represented, as the volume of a gas increases by the same fraction of its volume for every Kelvin increase in temperature when pressure is constant.

The thermal expansion of gases is a physical phenomenon that is well explained by Charles's Law. Essentially, as the temperature of a gas increases, so does its volume, provided that the pressure remains unchanged. This thermal expansion occurs due to an increase in the kinetic energy of the gas molecules, which results in the molecules moving faster and pushing outward more forcefully, causing an increase in volume.

Understanding this concept is crucial when solving problems involving the heating or cooling of a gas. One must take into account not only the change in temperature but also how this change affects the volume of the gas. In the context of the provided exercise, this means that the air expelled upon heating causes an increase in volume from the original state, thereby directly indicating a temperature increase.

IIT-JEE Chemistry problems are designed to test a student's conceptual understanding as well as their problem-solving skills in the field of chemistry. They involve a wide array of topics, including but not limited to, the thermal behavior of gases, the periodic table, chemical kinetics, and equilibrium.

The ability to apply gas laws, like Charles's Law, accurately in various scenarios is a significant aspect of the chemistry portion of the IIT-JEE exams. These problems often require multi-step solutions that involve temperature conversions, understanding the proportional relationships between variables, and a keen eye for detail when working through the provided data. In many cases, these problems are not merely a test of memorization, but rather an assessment of how well students can apply their knowledge to novel situations.