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70Cal heat is required to raise the temperature of 2 moles of an Ideal gas at constant pressure from 25°C to 30°C, then the amount of heat, required to raise the temperature of the same gas through the same rise of temp, at constant volume is


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Solution

The molar-specific heat of an ideal gas at constant pressure and volume are Cp and Cv respectively.

  1. The molar-specific heat of an ideal gas for the isobaric process(at constant pressure)
  • Cp=QnT
  • Where Q=Change in heat energy=70 Cal
  • T= Change in temperature=(30-25)°C
  • n= Given moles of substance= 2 mole
  • Cp=702×(30-25)=702×5=7010=7caloriesmole-1K-1
  • For an ideal gas Cp-Cv=R=8.314JMole×K2CalMole×K
  • Cv=Cp-R
  • Cv=7-2=5caloriesmole-1K-1

2. The molar-specific heat of an ideal gas for the isochoric process(at constant volume)

  • Cv=QnTQ=Cv×nT
  • Q=5×2×(30-25)Q=5×2×5Q=5×10Q=50calories

50 calories heat is required to raise the temperature of 2 Moles of an Ideal gas at a constant volume from 25°C to 30°C.


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