Explanation:
(a) First, we will calculate the number of moles as follows.
No. of moles = [tex]\frac{\text{mass}}{\text{molar mass}}[/tex]
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 = [tex]\frac{\text{mass}}{\text{molar mass}}[/tex]
= [tex]\frac{\text{100 g}}{4 g/mol}[/tex]
= 25 mol
According to the ideal gas equation,
PV = nRT
or, [tex](P_{2} - P_{1})V = nR (T_{2} - T_{1})[/tex]
[tex](6.90 atm - 3.45 atm) \times 200 L = 25 \times 0.0821 L atm/mol K \Delta T[/tex]
[tex]\Delta T[/tex] = 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 = [tex]mC \Delta T[/tex]
= [tex]100 g \times 5.193 J/g K \times 336.17 K[/tex]
= 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.
