Effect of Temperature on Gas Volume: Calculating Volume Change at Constant Pressure

In thermodynamics, the behavior of gases is one of the fundamental areas of study. Understanding the relationship between the volume and temperature of a gas at constant pressure is crucial for many practical applications. This relationship is encapsulated in Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin when pressure is held constant.

Charles's Law and the Ideal Gas Law

The core of this behavior is described by Charles's Law, which can be mathematically represented as:

(frac{V_1}{T_1} frac{V_2}{T_2})

Where:

(V_1) Initial volume of the gas (in liters or liters) (T_1) Initial temperature of the gas in Kelvin (K) (V_2) Final volume of the gas (in liters or liters) (T_2) Final temperature of the gas in Kelvin (K)

The Ideal Gas Law, which is a more comprehensive equation that accounts for the pressure and number of gas molecules, can also be useful in these calculations. It is given by:

(PV nRT)

Where:

P Pressure of the gas V Volume of the gas n Number of moles of the gas R Universal gas constant T Temperature of the gas in Kelvin

Calculating Volume at a Given Temperature

Given the scenario where 3 liters of a gas is cooled down from 15°C to -73°C at a constant pressure, we can use Charles's Law to determine the new volume of the gas. Here are the steps to achieve this calculation:

Convert temperatures to Kelvin: Initial temperature: (T_1 15°C 273.15 288.15 K) Final temperature: (T_2 -73°C 273.15 200.15 K)

Note that the conversion from Celsius to Kelvin is done using the formula (T(K) T(°C) 273.15).

Use Charles's Law:

Charles's Law tells us that (frac{V_1}{T_1} frac{V_2}{T_2}).

Rearranging the formula to solve for (V_2), we get:

(V_2 V_1 times frac{T_2}{T_1})

Substitute the known values:

Given:

(V_1 3) L (T_1 288.15) K (T_2 200.15) K

Therefore,

(V_2 3) L (times frac{200.15) K}{288.15) K} (approx 3) L (times 0.694) (approx 2.082) L

Conclusion

The volume of the gas when cooled from 15°C to -73°C at constant pressure will be approximately 2.08 liters. This calculation is an excellent example of how Charles's Law is applied in practical thermodynamic scenarios.

Understanding these principles is crucial for a wide range of applications, from weather predicting to determining the efficiency of gas-powered engines.

Keywords: Charles's Law, Ideal Gas Law, Temperature-Volume Relationship