Question

How many moles of photon would contain sufficient energy to raise the temperature of $225g$ of water $21$ to $96$? Specific heat of water is $4.18$ $J$ $g^{-1}{K}^{-1}$ and frequency of light radiation used is $2.45\times {10}^9{s}^{-1}$.

Answer 1

Energy associated with one mole of photons $=N_0\times h\times v$
$=6.02\times {10}^{23}\times 6.626\times {10}^{-34}\times 2.45\times {10}^9$
$=97.727\times {10}^{-2}J{mol}^{-1}$
Energy required to raise the temperature of $225g$ of water by $75=m\times s\times t=225\times 4.18\times 75=70537.5J$
Hence, number of moles of photons required $=\frac{mst}{N_{0}hv}=\frac{70537.5}{97.727\times {10}^{-2}}=7.22\times {10}^{4}mol$.