# Solving Isothermal Expansion Problem - Temperature Calculation

• morsel
In summary, the temperature at the beginning and end of the isothermal expansion process for 161 moles of a monatomic ideal gas is 5.98 K and 5979 K, respectively. This answer may seem large, but it is correct based on the given information and the gas law equation. The question itself may have been misleading in terms of units and conversions.
morsel

## Homework Statement

Suppose 161 moles of a monatomic ideal gas undergoes an isothermal expansion as shown in the figure (attached). The horizontal axis is marked in increments on 20 m3

What is the temperature at the beginning and at the end of this process?

PV = nRT

## The Attempt at a Solution

Pi = 400 kPa
Vi = 20 m3
Pf = 100 kPa
Vf = 80 m3

T = (PV)/(nR) = (400*20)/(161*8.31) = 5.98 K

My answer is wrong according to the online homework grading system. What am I doing wrong?
Any help is appreciated.

#### Attachments

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The pressure is kilo pascal.

OK. But even if I convert kPa to Pa and calculate, that's still not the answer.
T = (400,000 Pa * 20) / (161*8.31) = 5979 K
This seems outrageously large.

morsel said:
OK. But even if I convert kPa to Pa and calculate, that's still not the answer.
T = (400,000 Pa * 20) / (161*8.31) = 5979 K
This seems outrageously large.
True. But you can blame the person who drafted the question. That is the right answer to this question.

One mole of a gas at STP occupies 22.4 litres or .0224 m^3. That is at about 100 kPa pressure and a temperature of 273 K. Here, you have 161 times that amount of gas occupying 80/.0224 = 3571 times as much volume. So to reach the same 1 atm pressure the temperature has to be 3571/161 = 22 times the temperature at STP -about 6000 degrees.

AM

## 1. What is an isothermal expansion?

An isothermal expansion is a thermodynamic process in which a gas expands at a constant temperature. This means that the heat added or removed from the system is balanced by the work done by the gas, resulting in no change in temperature.

## 2. How do you calculate the temperature change during an isothermal expansion?

The temperature change during an isothermal expansion can be calculated using the ideal gas law, which states that the product of pressure and volume is directly proportional to the absolute temperature. Therefore, by knowing the initial and final volumes and pressures, the temperature change can be determined.

## 3. What factors affect the temperature during an isothermal expansion?

The temperature during an isothermal expansion is affected by the initial and final volumes and pressures of the gas, as well as the amount of heat added or removed from the system. Additionally, the type of gas and its specific heat capacity can also impact the temperature change.

## 4. How does an isothermal expansion differ from an adiabatic expansion?

An isothermal expansion occurs at a constant temperature, while an adiabatic expansion occurs without any heat exchange with the surroundings. This means that the temperature change during an adiabatic expansion will be greater than that of an isothermal expansion, as there is no heat added or removed to balance the work done by the gas.

## 5. What are some real-world applications of isothermal expansion?

Some common examples of isothermal expansion in real-world applications include the workings of a refrigerator, where a gas is compressed and expanded at a constant temperature to cool the interior, and the operation of steam engines, where steam expands isothermally to produce work.

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