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JEE MainPhysicsThermodynamics

For a given ideal gas, which of the following thermodynamic quantities is directly proportional to its absolute temperature T ?

Options

  1. AInternal energy per mole
  2. BThe difference between molar heat capacities, C_P - C_V
  3. CThe ratio of molar heat capacities, C_P C_V
  4. DThe number of degrees of freedom, f

Correct answer

A. Internal energy per mole

Step-by-step solution

For an ideal gas, the internal energy per mole is given by U = f 2 RT , which is directly proportional to the absolute temperature T . The difference between molar heat capacities is C_P - C_V = R , which is a universal constant. The ratio of molar heat capacities is C_P C_V = 1 + 2 f , which is constant for a given gas under standard conditions. The number of degrees of freedom f depends on the atomicity of the gas and is constant over standard temperature ranges. Answer: Internal energy per mole

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