If a gas with a pressure of 1 atm expands into a volume that is twice its original size and the temperature raises from 100 K to 400 K, what is the final pressure?

If a gas with a pressure of 1 atm expands into a volume that is twice its original size and the temperature raises from 100 K to 400 K, what is the final pressure?

• A. 0.5 atm
• B. 1 atm
• C. 2 atm
• D. 4 atm

Answer: (C)

To determine the final pressure of the gas after it expands and experiences a temperature change, we can use the ideal gas law and its principles. The ideal gas law states that for a given amount of gas under varying conditions, the relationship between pressure (P), volume (V), and temperature (T) can be expressed as \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \). In this scenario, the initial conditions include a pressure of 1 atm, an initial volume (V1), and an initial temperature of 100 K. After the expansion, the new volume (V2) is twice the original volume, which means \( V_2 = 2V_1 \). The final temperature is increased to 400 K. Plugging the known values into the formula: - Initial pressure (P1) = 1 atm - Initial volume (V1) = V1 - Initial temperature (T1) = 100 K - Final volume (V2) = 2V1 - Final temperature (T2) = 400 K - Final pressure (P2) is what we want to calculate

To determine the final pressure of the gas after it expands and experiences a temperature change, we can use the ideal gas law and its principles. The ideal gas law states that for a given amount of gas under varying conditions, the relationship between pressure (P), volume (V), and temperature (T) can be expressed as ( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} ).

In this scenario, the initial conditions include a pressure of 1 atm, an initial volume (V1), and an initial temperature of 100 K. After the expansion, the new volume (V2) is twice the original volume, which means ( V_2 = 2V_1 ). The final temperature is increased to 400 K.

Plugging the known values into the formula:

• Initial pressure (P1) = 1 atm

• Initial volume (V1) = V1

• Initial temperature (T1) = 100 K

• Final volume (V2) = 2V1

• Final temperature (T2) = 400 K

• Final pressure (P2) is what we want to calculate