The molar heat capacity of water at constant pressure `P` , is `75JK^(-1)mol^(-1)` . When `1.0KJ` of heat is supplied to `100g` of water which is free to expand, the increase in temperature of water is

Options

A. `6.6 K`
B. `1.2 K`
C. `2.4 K`
D. `4.8 K`

Answer

C

Explanation

Accroding to thermodynamics,
`q = nC_(m) Delta T`
where `n`is the number moles, `C_(m)` is the molar heat capacity, and `Delta T` is the temperature change.
`n = (Mass_(H_(2)O))/("Molar mass"_(H_(2)O))`
`= (100 g)/(18 g mol^(-1)) = 5.55 mol`
According to the above equation,
`Delta T = (q)/(nC_(m)) = (1000 J)/((5.55 mol)(75 J K^(-1) mol^(-1)))`
`= 2.4 K`