Why is \( C_V \) Relevant in Isothermal Expansion Calculations?

In summary, the problem is asking for the values of ΔU, ΔH, q, w, and final temperature (Tf) for an isothermal reversible expansion of one mole of an ideal monoatomic gas from an initial pressure of 10 atm to a final pressure of 1 atm at a constant temperature of 300 K. The molar heat capacity for constant volume, C_V, is given as 3/2(R). However, the relevance of C_V in this problem is unclear as the gas is expanding and thus not at constant volume. It is known that for an isothermal reversible expansion, ΔU = 0 and therefore q = -w. The work can be calculated using the formula nRTln(V_f
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Homework Statement


One mole of an ideal monoatomic gas initially at 300 K is expanded from an initial pressure of 10 atm to a final pressure of 1 atm. The molar heat capacity for constant volume for the gas is C_V = 3/2(R).
Calculate ΔU, ΔH, q, w, and the final temperature (Tf) for an isothermal reversible expansion



Homework Equations


I can't proceed with solving because i fail to see why C_V is relevent. It is for constant volume, but this is an expansion, so its not constant volume.
I know that final temp is 300K because problem specifies isothermal.
I know that internal energy is constant for isothermal reversible expansion; deltaU = 0
therefore q = -w
I know the work will = nRTln(V_f/V_i) but i don't know the volume change and also i don't know how to apply the C_V value.. please help. hint or something.. thanks


The Attempt at a Solution


 
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I can't proceed with solving because i fail to see why C_V is relevent. It is for constant volume, but this is an expansion, so its not constant volume.I know that final temp is 300K because problem specifies isothermal.I know that internal energy is constant for isothermal reversible expansion; deltaU = 0 therefore q = -w I know the work will = nRTln(V_f/V_i) but i don't know the volume change and also i don't know how to apply the C_V value.. please help. hint or something.. thanks
 

FAQ: Why is \( C_V \) Relevant in Isothermal Expansion Calculations?

What is isothermal expansion?

Isothermal expansion is a process in thermodynamics where the temperature of a system remains constant while it undergoes expansion. This means that the energy of the system remains constant, but the volume increases.

What is the equation for isothermal expansion?

The equation for isothermal expansion is PV = constant, where P is the pressure of the system and V is the volume. This equation is also known as Boyle's Law.

How does isothermal expansion differ from adiabatic expansion?

Isothermal expansion and adiabatic expansion are both thermodynamic processes, but they differ in that isothermal expansion occurs at a constant temperature while adiabatic expansion occurs with no exchange of heat with the surroundings. This means that the temperature of the system changes during adiabatic expansion.

What are some real-life examples of isothermal expansion?

One example of isothermal expansion is the expansion of a balloon when it is heated. The temperature of the air inside the balloon remains constant, but the volume increases as the air molecules gain energy and move further apart. Another example is the expansion of gas in a piston-cylinder system that is kept in contact with a heat reservoir, keeping the temperature constant.

How is isothermal expansion used in engineering and technology?

Isothermal expansion is used in a variety of engineering and technological applications, such as refrigeration systems, heat engines, and gas turbines. It is also an important concept in the design of engines and compressors, as it allows for more efficient energy transfer and utilization.

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