Solving for Heat Capacity and Ideal Gas Type in Thermodynamics

AI Thread Summary
The discussion focuses on solving a thermodynamics problem involving one mole of an ideal gas at 360K, which undergoes adiabatic expansion and isothermal compression. The goal is to determine the ratio C_p / C_v and identify the type of ideal gas, given a heat measurement of 1304J. Participants share their struggles with manipulating thermodynamic equations and expressing C_p and C_v in terms of known variables. Key equations mentioned include those for adiabatic and isothermal processes, which are essential for deriving the solution. Ultimately, the discussion highlights the challenges in applying thermodynamic principles to solve for specific heat capacities.
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Homework Statement


The temperature of one mole of ideal gas is 360K. The gas is allowed to expand adiabatically to the double volume. Then it is compressed isothermally to original volume. The specified amount of heat is measured at 1304J. Determine C_p / C_v, and specify the type of ideal gas were' talking about.


Homework Equations


So far I'v drawn a pressure/volume diagram and tried to express everything in terms of unknown p_1, unknown v_1 and known t_1. Then I'v kinda done just about anything I know in thermodynamics, but I'v got no clue in what I'm doing. I looked in the answers and just tried to manipulate my way the correct answer but so far I'm unsuccessful.
Another thing i tried is, since C_p and C_v is expressed in partial derivatives of the temperature and the last change in the gas was isothermic, i tried to manipulate the equations from that... right now I'm completely lost.



The Attempt at a Solution


No idea
 
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bhoom said:

Homework Statement


The temperature of one mole of ideal gas is 360K. The gas is allowed to expand adiabatically to the double volume. Then it is compressed isothermally to original volume. The specified amount of heat is measured at 1304J. Determine C_p / C_v, and specify the type of ideal gas were' talking about.

Homework Equations


So far I'v drawn a pressure/volume diagram and tried to express everything in terms of unknown p_1, unknown v_1 and known t_1. Then I'v kinda done just about anything I know in thermodynamics, but I'v got no clue in what I'm doing. I looked in the answers and just tried to manipulate my way the correct answer but so far I'm unsuccessful.
Another thing i tried is, since C_p and C_v is expressed in partial derivatives of the temperature and the last change in the gas was isothermic, i tried to manipulate the equations from that... right now I'm completely lost.

The Attempt at a Solution


No idea

Let's start with the relevant equations.

Let ##γ=\frac {C_p}{C_v}##.

In an adiabatic process ##TV^{γ-1}=constant##.
In an isothermal process ##Q=RT\ln \frac {V_1} {V_2}##.

You can find these equations for instance on wikipedia.Can you solve these equations for γ?
 
I like Serena said:
Let's start with the relevant equations.

Let ##γ=\frac {C_p}{C_v}##.

In an adiabatic process ##TV^{γ-1}=constant##.
In an isothermal process ##Q=RT\ln \frac {V_1} {V_2}##.

You can find these equations for instance on wikipedia.


Can you solve these equations for γ?

I got it now, thanks. My problem were how to express c_v and c_p.
 

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