4. A light bulb contains 0.0560 g of Argon gas with a pressure of 1.34 atm at 26.0 °C. The light bulb is then turned on and, after a period of time, the temperature rises to 179 °C. Calculate the final pressure inside the light bulb.
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![**Problem Statement:**
A light bulb contains 0.0560 g of Argon gas with a pressure of 1.34 atm at 26.0 °C. The light bulb is then turned on and, after a period of time, the temperature rises to 179 °C. Calculate the final pressure inside the light bulb.
**Explanation:**
This is a thermodynamics problem involving gases. Use the ideal gas law and the concept of the combined gas law to find the final pressure after a change in temperature.
- **Initial Conditions:**
- Mass of Argon gas = 0.0560 g
- Initial Pressure (P₁) = 1.34 atm
- Initial Temperature (T₁) = 26.0 °C = 299.15 K
- **Final Conditions:**
- Final Temperature (T₂) = 179 °C = 452.15 K
**Key Concepts:**
- Ideal Gas Law: PV = nRT
- Combined Gas Law: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \) (assuming volume and moles of gas are constant)
**Steps to Solve:**
1. Convert the given temperatures from Celsius to Kelvin by adding 273.15.
2. Use the combined gas law to calculate the final pressure (P₂):
\[
P_2 = P_1 \times \frac{T_2}{T_1}
\]
3. Insert the known values and solve for P₂.
This will give you the final pressure inside the light bulb after the temperature increase.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30f8b710-1a61-4c05-9269-dd497cde8c1e%2F3d22380a-743a-4ae3-a01a-f12ee674ec25%2Fgcdcc76_processed.jpeg&w=3840&q=75)
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