A given mass of gas occupies a certain volume at 300K. At what temperature will...
A given mass of gas occupies a certain volume at 300K. At what temperature will its volume be double?
- A) 400K
- B) 480K
- C) 550K
- D) 600K
Correct Answer: D) 600K
Explanation
To understand this question, let's first recall Charles's Law, which states that the volume of a gas is directly proportional to its temperature, provided that the pressure and the amount of gas remain constant. Mathematically, it can be represented as:
\(V_1 / T_1 = V_2 / T_2\)
Where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
In this question, we are given that the initial temperature (T1) is 300K, and we need to find the final temperature (T2) when the volume of the gas is doubled. Since the volume is doubled, we can write:
\(V_2 = 2 \times V_1\)Now, using Charles's Law, we can substitute this into the equation:
\(V_1 / 300K = (2 \times V_1) / T_2\)Notice that the volume (V1) can be canceled out from both sides:
\(1 / 300K = 2 / T_2\)Now, we can rearrange the equation to solve for T2:
\(T_2 = (2 \times 300K) / 1\)Which simplifies to:
\(T_2 = 600K\)So, the correct answer isOption D: 600K. At a temperature of 600K, the volume of the given mass of gas will be double its initial volume.