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(306 ~J ) of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from (25^ C ) to (35^ C ). The amount of heat required to raise the temperature of the same gas through the same range at constant volume is

Options

  1. A(306 ~J )
  2. B(153 ~J )
  3. C(140 ~J )
  4. D(80 ~J )

Correct answer

C. (140 ~J )

Step-by-step solution

Given, at constant pressure heat (Q_p=306 ~J ) Number of mole, (n=2 ) ( aligned T & =T₂-T₁ & =35-25=10^ C aligned ) We know that, (Q_p=n C_p T ) ( array ll & 306=2 C_p 10 & C_p= 306 2 10 & C_p=15.3 ~J / mol K array ) According to Mayer's formula, ( aligned & C_p-C_V =R & C_V =C_p-R=15.3-8.314 & C_V =6.986 ~J / mol K aligned ) The amount of heat required to raise the temperature of gas at constant volume through same range of temperature. ( aligned Q_V & =n C_V T & =2 6.986 (35-25) & =2 6.986 10 & =139.72 140 ~J ali

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