Published by:
CGP EDU Academic Team
Published on: September 13, 2026
A gas is confined inside a container having a movable piston. The gas is allowed to expand isobarically. If the initial volume of gas is
and the speed of sound in the gas is
, then the speed of sound when the volume of the gas increases to
is
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: Recognize that the speed of sound in a gas is given by the equation: \( v = \sqrt{\frac{\gamma R T}{M}} \), where \( v \) is the speed of sound, \( \gamma \) is the adiabatic index, \( R \) is the universal gas constant, \( T \) is the temperature of the gas, and \( M \) is the molar mass of the gas.
Step 2: In an isobaric process, the pressure remains constant while the volume and temperature of the gas can change. Given that the volume increases can lead to an increase in temperature for the gas (as it absorbs heat).
Step 3: Determine the relationship between initial and final conditions for the gas. If the initial speed of sound is \( v_1 \) at initial volume \( V_1 \) and the final volume is \( V_2 \), we know \( v_1 = \sqrt{\frac{\gamma R T_1}{M}} \) and will assess \( v_2 = \sqrt{\frac{\gamma R T_2}{M}} \).
Step 4: If the temperature increases linearly with volume at constant pressure, we can say that if \( V_1 \) increases to \( V_2 \), then the speed of sound will also increase accordingly.
Step 5: Thus, if the second speed of sound needs to be calculated using the same initial values with new volume and an increased temperature, we would find that the answer is represented in option D.
Therefore, the correct answer is D.
Step 2: In an isobaric process, the pressure remains constant while the volume and temperature of the gas can change. Given that the volume increases can lead to an increase in temperature for the gas (as it absorbs heat).
Step 3: Determine the relationship between initial and final conditions for the gas. If the initial speed of sound is \( v_1 \) at initial volume \( V_1 \) and the final volume is \( V_2 \), we know \( v_1 = \sqrt{\frac{\gamma R T_1}{M}} \) and will assess \( v_2 = \sqrt{\frac{\gamma R T_2}{M}} \).
Step 4: If the temperature increases linearly with volume at constant pressure, we can say that if \( V_1 \) increases to \( V_2 \), then the speed of sound will also increase accordingly.
Step 5: Thus, if the second speed of sound needs to be calculated using the same initial values with new volume and an increased temperature, we would find that the answer is represented in option D.
Therefore, the correct answer is D.
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