Question

A fixed amount of ideal gas is at temperature 25°C, volume 4.0 L, and pressure 100 kPa. The temperature of the gas is increased to 80°C while the volume is decreased to 3.2 L. Determine the new pressure.

Answer 1

The new pressure of the ideal gas after the temperature is increased from 25°C to 80°C and the volume is decreased from 4.0 L to 3.2 L is approximately 139.1 kPa.

Step-by-step explanation:

To determine the new pressure of the ideal gas after a change in volume and temperature, we can use the combined gas law, which is derived from the ideal gas law (PV = nRT). The combined gas law is:

P1V1/T1 = P2V2/T2 where P is pressure, V is volume, and T is temperature in Kelvin.

First, we must convert all temperatures to Kelvin by adding 273.15 to the Celsius values. Therefore, 25°C becomes 298.15 K and 80°C becomes 353.15 K.

Using the given values:

P1 = 100 kPa (initial pressure)V1 = 4.0 L (initial volume)T1 = 298.15 K (initial temperature)V2 = 3.2 L (final volume)T2 = 353.15 K (final temperature)

Replace everything into the combined gas law equation:

(100 kPa)(4.0 L)/(298.15 K) = P2(3.2 L)/(353.15 K)

After rearrangement, we find P2 :

P2 = ((100 kPa)(4.0 L)/(298.15 K)) * (353.15 K)/(3.2 L)
P2 ≈ 139.1 kPa (new pressure)