Two moles of oxygen is mixed with one moles of helium. The effective specific heat of the mixture at constant volume is:

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  1. 1.7 R
  2. 2.17 R
  3. 2.7 R
  4. 3 R

Answer (Detailed Solution Below)

Option 2 : 2.17 R
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CONCEPT:

  • The molar specific heat capacity of a gas at constant volume is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.

  • The molar specific heat of a gas at constant pressure is defined as the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.

  • The relation between the ratio of Cp and Cv with a degree of freedom is given by

Where f = degree of freedom

  • The molar specific heat of gaseous mixture at constant volume is given by the formula:

Where n1 and n2 are moles of the gases.

CALCULATION:

Given: n1 = 2 and n2 = 1

  • Oxygen is a diatomic gas, therefore the molar specific heat capacity of a gas at constant volume is 

  • Helium is a monoatomic gas, therefore the molar specific heat capacity of a gas at constant volume is 

  • The effective specific heat of the mixture at constant volume is

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