Question

A sealed cylinder fitted with a movable piston contains ideal gas at 27°C, pressure 0.500 × 10⁵ Pa, and volume 1.25 m³. What will be the final temperature if the gas is compressed to 0.800 m³ and the pressure rises to 0.820 × 10⁵ Pa?

A) 42°C
B) 68°C
C) 130°C
D) 250°C
E) 150°C

Answer 1

The final temperature of the compressed ideal gas is 130°C. This is calculated using the combined gas law and converting temperatures between Celsius and Kelvin.The correct option is option c .

Step-by-step explanation:

The final temperature of an ideal gas when it is compressed can be determined using the combined gas law, which is a combination of Boyle's Law, Charles's Law, and Gay-Lussac's Law. The combined gas law is expressed as (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is temperature in Kelvin.

To find the final temperature (T2) of the gas when the volume is changed to 0.800 m³ and the pressure is increased to 0.820 × 10⁵ Pa, we first need to convert the initial temperature from Celsius to Kelvin. Therefore, T1 = 27°C + 273.15 = 300.15 K. Now, we apply the combined gas law:

(0.500 × 10⁵ Pa * 1.25 m³) / 300.15 K = (0.820 × 10⁵ Pa * 0.800 m³) / T2

This gives us T2 = (0.820 × 10⁵ × 0.800) / (0.500 × 1.25) * 300.15 K = 403.15 K.

To convert Kelvin back to Celsius, subtract 273.15 from the Kelvin temperature. T2 = 403.15 K - 273.15 = 130°C. Therefore, the final temperature of the ideal gas after compression is 130°C, which corresponds to option C).