Question

question 15 of 30
charless law describes the relationship of the volume and temperature of
gas at a constant mass and pressure. according to this law, what would
happen to the volume of the gas if its temperature decreased from 400 k to
300 k?

a. the volume would increase by 100 ml.

b. the volume would be 4/3 of its original value.

c. the volume would be 3/4 of its original value.

d. the volume would decrease from 400 ml to 300 ml.

Explanation:

Step1: Recall Charles's Law

Charles's Law states that for a gas at constant pressure and mass, the volume \( V \) is directly proportional to the absolute temperature \( T \) (in Kelvin), i.e., \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \), where \( V_1, T_1 \) are initial volume and temperature, and \( V_2, T_2 \) are final volume and temperature.

Step2: Substitute given temperatures

Given \( T_1 = 400\space K \) and \( T_2=300\space K \). From \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \), we can solve for \( V_2 \): \( V_2=\frac{T_2}{T_1}V_1 \).
Substitute \( T_1 = 400 \) and \( T_2 = 300 \): \( V_2=\frac{300}{400}V_1=\frac{3}{4}V_1 \). So the volume becomes \( \frac{3}{4} \) of its original value.

Answer:

C. The volume would be 3/4 of its original value.