Question:
The temperature of a given mass of an ideal gas is changed from 27^ to 327^ at constant pressure. If the initial volume of the gas is V, then its final volume will be:
The temperature of a given mass of an ideal gas is changed from 27^ to 327^ at constant pressure. If the initial volume of the gas is V, then its final volume will be:
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Never substitute temperature values in Celsius directly into gas law ratios! For example, using 32727 = 12.11 would lead to a completely incorrect answer. Always convert to Kelvin first.
Updated On: Jun 10, 2026
- 2V
- 3V
- 4V
- V2
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The Correct Option is A
Solution and Explanation
Concept:
For a given mass of an ideal gas, the relationship between its pressure (P), volume (V), and absolute temperature (T) is governed by the Ideal Gas Law:
where n is the number of moles and R is the universal gas constant.
When the gas undergoes a thermodynamic process at constant pressure ( P = 0), the process is termed isobaric. Under isobaric conditions, the volume of a fixed mass of gas is directly proportional to its absolute temperature. This principle is famously known as Charles's Law:
A critical requirement when applying gas laws is that temperature values must always be expressed on the absolute thermodynamic scale, i.e., in Kelvin (K). The conversion from degrees Celsius (^) to Kelvin (K) is given by:
Step 1: Converting Temperatures to the Kelvin Scale
Let us compute the initial absolute temperature (T_1) and final absolute temperature (T_2):
Step 2: Setting up Charles's Law Equation
The problem defines the initial volume of the gas as V_1 = V. We need to find the final volume V_2. Rearranging Charles's Law to isolate the final volume variable V_2:
Step 3: Calculating the Numerical Value of Final Volume
Substitute the temperature values into the ratio expression: Hence, when the absolute temperature is exactly doubled under constant pressure, the volume occupied by the gas also expands to twice its initial value.
Step 1: Converting Temperatures to the Kelvin Scale
Let us compute the initial absolute temperature (T_1) and final absolute temperature (T_2):
Step 2: Setting up Charles's Law Equation
The problem defines the initial volume of the gas as V_1 = V. We need to find the final volume V_2. Rearranging Charles's Law to isolate the final volume variable V_2:
Step 3: Calculating the Numerical Value of Final Volume
Substitute the temperature values into the ratio expression: Hence, when the absolute temperature is exactly doubled under constant pressure, the volume occupied by the gas also expands to twice its initial value.
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