Degrees of Freedom and Molar Specific Heats

In summary, the conversation was about giving 70J of heat to a diatomic gas and how much the internal energy of the gas would increase. The solution involved using the equations for heat and internal energy, and determining the ratio of specific heat for a diatomic gas to find the answer of 50J. The asker confirmed that the solution was correct and thanked the respondent for their help.
  • #1
mit_hacker
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0

Homework Statement



We give 70J as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase.

Homework Equations





The Attempt at a Solution



I did it this way:
Heat added = nCp dT = 70J.
Let Internal energy = nCv dT = x (say).
Dividing both equations, we obtain:
Cp/Cv = 70/x.
But, Cp/Cv is nothing but the ration of speicifc heat which for a diatomic gas is known to be 7/5. So, x = 50J.

Am I correct? the solution is not given in the book!

Thanks a ton in advance!
 
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  • #2
It is an isobaric process.

Your answer is 100% correct.
 
  • #3
Thanks a ton!

Thank-you so very much. I really appreciate it.
 

Related to Degrees of Freedom and Molar Specific Heats

1. What are degrees of freedom in thermodynamics?

Degrees of freedom in thermodynamics refer to the number of independent variables required to describe the state of a system. In other words, it is the number of parameters that can vary without changing the state of the system. In the context of gases, degrees of freedom refer to the number of ways in which the molecules can move and store energy.

2. How are degrees of freedom related to the molar specific heat?

The molar specific heat of a substance is defined as the amount of heat required to raise the temperature of one mole of the substance by one degree. The number of degrees of freedom of a substance determines the value of its molar specific heat. For example, for a monatomic gas, which has only translational motion, the degrees of freedom are 3 and the molar specific heat is 3R (where R is the gas constant). In contrast, for a diatomic gas, which has both translational and rotational motion, the degrees of freedom are 5 and the molar specific heat is 5R/2.

3. How do degrees of freedom and molar specific heat affect the behavior of gases?

The degrees of freedom and molar specific heat of a gas play a crucial role in determining its thermal and mechanical properties. For instance, gases with higher degrees of freedom and molar specific heat have a higher capacity to store energy and thus can absorb more heat before their temperature increases. This results in a slower change in temperature and makes these gases good insulators. On the other hand, gases with lower degrees of freedom and molar specific heat, such as monatomic gases, have a lower capacity to store energy and thus heat up faster, making them good conductors of heat.

4. How do degrees of freedom and molar specific heat vary with temperature?

The degrees of freedom and molar specific heat of a substance generally remain constant at low temperatures. However, as the temperature increases, the degrees of freedom may increase due to the excitation of rotational and vibrational modes of the molecules. This leads to an increase in the molar specific heat, as more energy is required to raise the temperature of the substance. At very high temperatures, the degrees of freedom may decrease as some modes of motion become unavailable, resulting in a decrease in the molar specific heat.

5. How are degrees of freedom and molar specific heat used in thermodynamic calculations?

Degrees of freedom and molar specific heat are important parameters in thermodynamic calculations, such as determining the change in internal energy and enthalpy of a system. They are also used in the calculation of the heat capacity ratio, which is the ratio of the molar specific heat at constant pressure to that at constant volume. Additionally, these parameters are crucial in understanding the behavior of gases in various thermodynamic processes, such as isothermal, adiabatic, and isochoric processes.

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