# Adiabatic, Isothermal and Isochoric Processes

• jlhannah
In summary, an ideal gas with a specific heat capacity of (5/2)R and a ratio of specific heats of 1.40 undergoes an adiabatic expansion, isothermal contraction, and isochoric heating. The pressure and volume at each step are given, and the number of moles and final temperature are calculated. The heat during the isochoric heating is found to be 1.5 * 10^5 J, but the correct answer is 1.6 * 10^5 J due to rounding error.
jlhannah

## Homework Statement

An ideal gas with Cv = (5/2)R, and Υ = 1.40 undergoes an adiabatic expansion until it has a pressure of 1.0*10^5 Pa and a volume of 2.0m^3. It then undergoes an isothermal contraction of T=300K until it has a volume of 1.0m^3, and then undergoes an isochoric (constant volume) heating until it reaches its original pressure and temperature.

What is Q during the isochoric heating?

## Homework Equations

These are the previous questions that I have already answered and know are correct.

What is the pressure in the gas before the start of the adiabatic expansion?
2.6*10^5 Pa

How much work is done by the gas during the isothermal contraction?
-1.4*10^5 J

## The Attempt at a Solution

At the start of the isothermal contraction (number of moles)-
PV = nRT
n = PV/RT
n = (1.0*10^5)(2.0)/(8.314)(300)
n = 80.19

At the start of the adiabatic expansion (finding final temp for isochoric heating)–
PV = nRT
T = PV/nR
T = (2.6*10^5)(1.0)/(8.314)(80.19)
T = 389.98

For the isochoric heating –

Q = nCvΔT
=(80.19)(5/2)(8.314)(389.98 – 300)
= 1.5*10^5 J

The correct answer is 1.6 * 10^5 J, so I am not really sure where I have gone wrong!

You rounded off the initial pressure too early. Keep two more digits.

ehild

## 1. What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no transfer of heat between the system and its surroundings. This means that the energy of the system is conserved and there is no change in the internal temperature of the system.

## 2. How does an isothermal process differ from an adiabatic process?

An isothermal process is a thermodynamic process in which the system's temperature remains constant throughout the process. This is achieved by transferring heat to or from the system to balance out any changes in temperature. In contrast, an adiabatic process does not allow for any heat transfer and therefore, the system's temperature may change.

## 3. What is an isochoric process?

An isochoric process is a thermodynamic process in which the volume of the system remains constant. This means that the system's boundary is fixed and there is no change in its volume. An isochoric process can occur under constant pressure, where any increase in temperature is balanced out by a decrease in density.

## 4. Can a process be both adiabatic and isothermal?

No, a process cannot be both adiabatic and isothermal at the same time. Adiabatic processes do not allow for heat transfer, while isothermal processes require heat transfer to maintain a constant temperature. However, a process can be both adiabatic and isochoric, or isothermal and isochoric.

## 5. What are some real-life examples of adiabatic, isothermal, and isochoric processes?

Examples of adiabatic processes include the compression or expansion of a gas in a piston without any heat transfer. An example of an isothermal process is the melting of ice in a glass of water, where heat is continuously transferred to maintain a constant temperature. An isochoric process can be seen in a pressure cooker, where the volume remains constant as the pressure increases to cook food faster.

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