A gas is suddenly compressed to 1/4th of itsOriginal volume at normal temp the increase In its temperature is (`/=1.5)

When a gas is compressed to a fraction of its original volume under constant temperature conditions, we can analyze the situation using the principles of thermodynamics and the ideal gas law. In this case, the gas is compressed to one-fourth of its original volume, and you're interested in understanding the effect this has on its temperature.

The Ideal Gas Law and Compression

The ideal gas law is represented as:

PV = nRT

• P = pressure of the gas
• V = volume of the gas
• n = number of moles of gas
• R = ideal gas constant
• T = absolute temperature of the gas

When the volume of a gas decreases, as in your scenario where it is compressed to 1/4th of its original volume, the pressure will increase if the number of moles and the temperature remain constant. However, if the gas is compressed suddenly, it may not be an isothermal process (constant temperature). Instead, we can expect an increase in temperature due to the work done on the gas.

Understanding the Temperature Change

If we apply the concept of adiabatic processes, where no heat is exchanged with the surroundings, the temperature of the gas will rise as a result of the compression. The relationship between the change in temperature and volume can be described mathematically, but a simplified understanding is that compressing a gas increases its internal energy, which in turn raises its temperature.

Mathematical Relation

In your case, you mentioned that the temperature increase is proportional to a factor of 1.5. This can be expressed as:

T_final = T_initial × 1.5

This means that if you know the initial temperature of the gas, you can easily calculate the final temperature after compression. For instance, if the initial temperature was 300 K, then:

T_final = 300 K × 1.5 = 450 K

Practical Implications

This behavior is commonly observed in various applications, such as in internal combustion engines where air-fuel mixtures are compressed in the cylinder before ignition, leading to a temperature rise that aids in combustion. Understanding this principle is crucial for engineers and scientists working with gases in different environments.

Summary

The compression of a gas to one-fourth of its original volume leads to an increase in temperature due to the work done on the gas. The final temperature can be determined by multiplying the initial temperature by the factor indicating temperature increase, which in your case is 1.5. This principle plays a significant role in various scientific and engineering fields, illustrating the interplay between pressure, volume, and temperature in gases.