Question:

Case-1: An ideal gas of molecular weight M at temperature T.
Case-2: Another ideal gas of molecular weight 2M at the temperature \(\frac{T}{2}\).
Identify the correct statement in the context of the above two cases.

Updated On: Jul 14, 2023
  • Average kinetic energy and average speed will be the same in the two cases. 
  • Both the averages are halved
  • Both the averages are doubled.
  • Only average speed is halved in the second case.
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The Correct Option is B

Solution and Explanation

The correct answer is option (B): Both the averages are halved
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Concepts Used:

Ideal Gas Equation

An ideal gas is a theoretical gas composed of a set of randomly-moving point particles that interact only through elastic collisions.

What is Ideal Gas Law?

The ideal gas law states that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant.

PV=nRT

where,

P is the pressure

V is the volume

n is the amount of substance

R is the ideal gas constant

Ideal Gas Law Units

When we use the gas constant R = 8.31 J/K.mol, then we have to plug in the pressure P in the units of pascals Pa, volume in the units of m3 and the temperature T in the units of kelvin K.