Question

\(V_0\) and \(V_t\) are volumes of an ideal gas at \(0 ^{\circ}\text{C}\) and \(t ^{\circ}\text{C}\) respectively, find ratio \(\frac{V_t}{V_0}\)

• A. \(\frac{1}{273}\times t\)
• B. \(1+273\times t\)
• C. \(1+\frac{t}{273}\)
• D. \(\frac{1}{273+t}\)

Hint:

Charles's law gives \(V_t = V_0\left(1+\frac{t}{273}\right)\) at constant pressure.

Answer 1

The Correct Option is C

Step 1: Use absolute temperature
Since $V\propto T$, $\dfrac{V_t}{V_0}=\dfrac{273+t}{273}$.

Step 2: Simplify
\[ \frac{273+t}{273} = 1+\frac{t}{273} \]
This is option (C).

Final Answer:
The ratio is $1+t/273$, option (C). \[ \boxed{1+\dfrac{t}{273}} \]