Question

A mass of 0.1 kg of helium fills a 0.2 m3 rigid tank at 350 kPa. The vessel is heated until the pressure is 700 kPa. Calculate the a) the temperature change of helium [deg. C], and b) the total amount of heat required for this process [kJ].

Answer 1

Step-by-step explanation:

(a) First, we will calculate the number of moles as follows.

No. of moles =
`\frac{\text{mass}}{\text{molar mass}}`

Molar mass of helium is 4 g/mol and mass is given as 0.1 kg or 100 g (as 1 kg = 1000 g).

Putting the given values into the above formula as follows.

No. of moles =
`\frac{\text{mass}}{\text{molar mass}}`

=
`\frac{\text{100 g}}{4 g/mol}`

= 25 mol

According to the ideal gas equation,

PV = nRT

or,
`(P_(2) - P_(1))V = nR (T_(2) - T_(1))`

`(6.90 atm - 3.45 atm) * 200 L = 25 * 0.0821 L atm/mol K \Delta T`

`\Delta T` = 336.17 K

Hence, temperature change will be 336.17 K.

(b) The total amount of heat required for this process will be calculated as follows.

q =
`mC \Delta T`

=
`100 g * 5.193 J/g K * 336.17 K`

= 174573.081 J/K

or, = 174.57 kJ/K (as 1 kJ = 1000 J)

Therefore, the amount of total heat required is 174.57 kJ/K.