Question

A gas sample enclosed in a rigid metal container at room temperature (20.0∘C) has an absolute pressure p₁. The container is immersed in hot water until it warms to 40.0∘C. What is the new absolute pressure p₂ ?

Express your answer in terms of p₁.
p₂ = 1.0682p₁

Answer 1

The new absolute pressure P₂ after heating a gas sample from 20.0°C to 40.0°C in a rigid container is calculated according to Gay-Lussac’s Law, yielding P₂ = 1.0682×P1.

Step-by-step explanation:

The question involves the application of the gas laws, specifically the relationship between pressure and temperature described by Gay-Lussac’s Law in a situation where a gas sample in a rigid container is subjected to a temperature change. According to Gay-Lussac’s Law, pressure of a gas is directly proportional to the absolute temperature when volume is held constant. As temperature increases, the absolute pressure inside the container also increases.

Given that the initial temperature T1 is 20.0°C (or 293.15 K) and the final temperature T₂ is 40.0°C (or 313.15 K), we can use the formula P₂= P1 × (T₂ / T₁) to find the new pressure P₂. This yields P₂ = 1.0682×P1.