Question

A gas at \(10\,^{\circ}\text{C}\) occupies a volume of 283 mL. if it is heated to \(20\,^{\circ}\text{C}\) keeping the pressure constant. What is the new volume of gas ?

• A. \(566\text{ mL}\)
• B. \(450\text{ mL}\)
• C. \(350\text{ mL}\)
• D. \(293\text{ mL}\)

Hint:

At constant pressure the volume is proportional to the Kelvin temperature.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute (Kelvin) temperature. This is Charles' law.

Step 2: Key Formula or Approach:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Convert the temperatures: \(T_1 = 10 + 273 = 283\) K and \(T_2 = 20 + 273 = 293\) K.

Step 3: Detailed Explanation:
\[ V_2 = V_1\times\frac{T_2}{T_1} = 283\times\frac{293}{283} = 293\text{ mL} \]
Doubling the Celsius temperature would wrongly give 566 mL (option A), but Charles' law needs Kelvin. The volume rises by only about 3.5 percent, so 450 and 350 mL are far too large.

Final Answer:
The new volume is 293 mL, option (D). \[ \boxed{293\text{ mL}} \]