The molar heat capacity of silver, measured at atmospheric pressure, is found to vary with temperature between 50 and 100 K by the empirical equation C = 0.318T – 0.00109T² – 0.628,where C is in J/mol . K and T is in K. Calculate the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K. the molar mass of silver is 107.87 g/mol.

To obtain Q, substitute 0.318T – 0.00109T² -0.628 for C in the equation Q = n ∫ CdT, we get,
Q = n ∫⁹⁰ K₅₀ K CdT
= n [(0.318 J/mol.K²) T²/2 – (0.00109 J/mol.K³) T³/3 –(0.628 J/mol.K)T] ⁹⁰ K₅₀ K
= n (645.8 J/mol)
As the molar mass of silver is 107.87 g/mol, thus the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K will be,
Q = n (645.8 J/mol)
= [316 g/(107.87 g/mol)] (645.8 J/mol)
=189 J
From the above observation we conclude that, the quantity of heat required to raise 316 g of silver from 50.0 to 90.0 K would be 189 J.