How Is Heat Calculated for an Ideal Gas at Constant Volume?

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SUMMARY

The discussion focuses on calculating the total heat added to an ideal gas at constant volume when the pressure changes from ##P_i## to ##P_f##. The key equation derived is ##Q=nC_v(T_f-T_i)##, where ##C_v## represents the molar heat capacity and ##n## is the number of moles of the gas. The relationship between pressure, volume, and temperature is established through the ideal gas law, ##PV=nRT##. This analysis confirms that the heat transfer is directly related to the change in temperature of the gas.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Knowledge of molar heat capacity (C_v)
  • Familiarity with thermodynamic principles
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the Ideal Gas Law and its applications
  • Learn about the significance of molar heat capacities in thermodynamics
  • Explore the relationship between pressure, volume, and temperature changes in gases
  • Investigate the implications of constant volume processes in thermodynamic cycles
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone interested in understanding heat transfer in ideal gases under constant volume conditions.

diredragon
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Homework Statement


An ideal gass is at constant volume risen to a new pressure level of ##P_f##. Find te expression for the total heat brought to the system.

Homework Equations


3. The Attempt at a Solution [/B]
So ##PV=nRT## and ##E=Q## ##Q=C_v(T_f-T_i)## so i just have to find ##(P_f-P_i)V=nR(Tf-Ti)## with the last term being what i need...?
 
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diredragon said:

Homework Statement


An ideal gass is at constant volume risen to a new pressure level of ##P_f##. Find te expression for the total heat brought to the system.

Homework Equations


3. The Attempt at a Solution [/B]
So ##PV=nRT## and ##E=Q## ##Q=C_v(T_f-T_i)## so i just have to find ##(P_f-P_i)V=nR(Tf-Ti)## with the last term being what i need...?
The equations you have written can be used, provided you write ##Q=nC_v(T_f-T_i)##, where Cv is the molar heat capacity and n is the number of moles.
 
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