The molar heat capacity of water at constant pressure, C, is 75 J K⁻¹ mol⁻¹. When 1.0 kJ of heat is supplied to 100 g of water which is free to expand, the increase in temperature of the water is:
1.2 K
2.4 K
4.8 K
6.6 K
Given: Molar heat capacity of water at constant pressure, C_p = 75 J K⁻¹ mol⁻¹ Heat supplied, q = 1.0 kJ = 1000 J Mass of water, m = 100 g Molar mass of water, M = 18 g mol⁻¹
Number of moles of water, n = m / M = 100 / 18 mol
The heat supplied at constant pressure is given by the formula: q = n × C_p × ∆T
Substituting the values: 1000 = (100 / 18) × 75 × ∆T ∆T = (1000 × 18) / (100 × 75) ∆T = 180 / 75 = 2.4 K
Thus, the increase in temperature of the water is 2.4 K.
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