Question

A gas has a pressure of 730 kPa at 96°C. What will the pressure be at 45°C?

P1T2 = P2T1

Group of answer choices

360 kPa

630 kPa

850 kPa

1600 kPa

Answer 1

630 kPa

Step-by-step explanation:

Given data

• Initial pressure (P₁): 730 kPa

• Initial temperature (T₁): 96 °C

• Final pressure (P₂): ?

• Final temperature (T₂): 45 °C

Step 1: Convert the temperatures to the absolute scale (Kelvin)

When working with gases, we always need to convert the temperatures to the Kelvin scale. We will use the following expression.

K = °C + 273.15

T₁: K = 96 °C + 273.15 = 369 K

T₂ = K = 45 °C + 273.15 = 318 K

Step 2: Calculate the final pressure

We will use Gay-Lussac's law.

`P_1 * T_2 = P_2 * T_1\\P_2 = (P_1 * T_2)/(T_1) = (730kPa * 318K)/(369K) = 630 kPa`