Solving for Heat Capacity and Ideal Gas Type in Thermodynamics

In summary: So γ=1.4 for diatomic gas.In summary, the conversation discusses determining the value of gamma (γ), the ratio of specific heats (C_p/C_v) for an ideal gas, and the type of ideal gas being discussed. The equations used for this problem are the adiabatic process equation (TV^(γ-1) = constant) and the isothermal process equation (Q = RT ln(V_1/V_2)). The conversation also mentions using wikipedia as a resource for these equations. The solution for γ is found to be 1.4 for a diatomic gas.
  • #1
bhoom
15
0

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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  • #2
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?
 
  • #3
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.
 

What is heat capacity?

Heat capacity is a measure of the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin).

How is heat capacity different from specific heat?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree, regardless of the amount of substance. Specific heat, on the other hand, is the amount of heat energy required to raise the temperature of one gram of a substance by one degree.

What factors affect the heat capacity of a substance?

The heat capacity of a substance is affected by its mass, composition, and phase. Substances with a higher mass, more complex molecular structures, and those in a solid or liquid phase tend to have higher heat capacities.

How is heat capacity measured?

Heat capacity can be measured experimentally by applying a known amount of heat to a substance and measuring the resulting change in temperature. The heat capacity can then be calculated using the formula Q = mcΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.

What is the relationship between heat capacity and temperature?

Heat capacity is dependent on temperature, as it takes more energy to raise the temperature of a substance at higher temperatures. As a substance approaches absolute zero (0 Kelvin), its heat capacity approaches zero as well.

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