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

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,       $(P_{2} - P_{1})V = nR (T_{2} - T_{1})$

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

          $\Delta T$ = 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 = $mC \Delta T$

                      = $100 g \times 5.193 J/g K \times 336.17 K$

                      = 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.