Question

At a constant volume, a gas exerts a pressure of 660 kPa at 602 ºC. At what temperature, in Celsius, will the pressure reduce to 330 kPa?

Answer 1

165 °C

Step-by-step explanation:

Given data

• Initial pressure (P₁): 660 kPa

• Initial temperature (T₁): 602 °C

• Final pressure (P₂): 330 kPa

• Final temperature (T₂): ?

Step 1: Convert the initial temperature to Kelvin

When working with gases, we always have to use the Kelvin scale. We can convert from Celsius to Kelvin using the following expression.

`K = \°C + 273.15\\K = 602 + 273.15 = 875 K`

Step 2: Calculate the final temperature

We will use the Gay-Lussac's law.

`(P_1)/(T_1) =(P_2)/(T_2)\\T_2 = (P_2 * T_1 )/(P_1) = (330 kPa * 875K )/(660kPa)=438K`

Step 3: Convert the final temperature to Celsius

`K = \° C + 273.15\\ \° C = K - 273.15 = 438 - 273.15 = 165 \° C`