Question

A compression, at a constant pressure of 140 kPa, is performed on 4.0 moles of an ideal monatomic gas (Cv = 3/2 R). The compression reduces the volume of the gas from 0.26 m^3 to 0.12 m^3. The change in the internal energy of the gas, in kJ is _____? ("^3" means to the power of 3)

Answer 1

Answer: The change in internal energy of the gas is 29.414 kJ.

Step-by-step explanation:

To calculate the temperature of the gas at different volumes, we use ideal gas equation:

`PV=nRT`

• When volume =
  `0.26m^3`

We are given:

Conversion used:
`1m^3=1000L`

`P=140kPa\\V=0.23m^3=260L\\n=4.0mol\\R=8.31\text{L kPa }mol^(-1)K^(-1)`

Putting values in above equation:

`140kPa* 260L=4mol* 8.31\text{L kPa }mol^(-1)K^(-1)* T_i\\\\T_i=1095.06K`

• When volume =
  `0.12m^3`

We are given:

`P=140kPa\\V=0.12m^3=120L\\n=4.0mol\\R=8.31\text{L kPa }mol^(-1)K^(-1)`

Putting values in above equation:

`140kPa* 120L=4mol* 8.31\text{L kPa }mol^(-1)K^(-1)* T_f\\\\T_f=505.41K`

• To calculate the change in internal energy, we use the equation:

`\Delta U=nC_v\Delta T=nC_v(T_f-T_i)`

where,

`\Delta U` = change in internal energy = ?

n = number of moles = 4.0 mol

`C_v` = heat capacity at constant volume =
`(3)/(2)R`

`T_f` = final temperature = 1095.06 K

`T_i` = initial temperature = 505.41 K

Putting values in above equation, we get:

`\Delta U=4* (3)/(2)* 8.314J/K.mol* (505.41-1095.06)\\\\\Delta U=29414.1J`

Converting this value in kilojoules, we use the conversion factor:

1 kJ = 1000 J

So,
`29414.1J=(1kJ)/(1000J)* 29414.1J=29.414kJ`

Hence, the change in internal energy of the gas is 29.414 kJ.