Question

Specific heat of water is $4.2J/g^{o}C$. If light of frequency $3\times {10}^{9}Hz$ is used to heat $400gm$ of water from ${20}^{o}C$ to ${40}^{o}C$, the number of photons needed will be?

• A. $1.69\times {10}^{29}$
• B. $1.69\times {10}^{28}$
• C. $2.80\times {10}^4$
• D. $2.80\times {10}^5$

Answer 1

Answer: (B)

$1.69\times {10}^{28}$

Given specific heat =4.2 J/g ${}^{0}c$ frequency $\nu$=3$\times {10}^9$Hz ;

$T_{1}and{T}_2$=20 and 40 degree celcius respectively.

Energy of each photon

$E_P=h\nu =(6.62\times {10}^{-34})\times (3\times {10}^9)=19.86\times {10}^{-25}$ J

Energy absorbed by water to increase its temperature by 20 degree Celsius

$=m{c}_p△T=400\times 4.2\times (40-20)=33.6\times {10}^3$ J

Number fof photons needed

$=\frac{E}{E_P}=\frac{33.6\times {10}^3}{19.86\times {10}^{-25}}=1.69\times {10}^{28}$