Specific heat of water is 4.2 , J/g^{circ}C. | vedclass

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Question

(B) Given:Specific heat of water,$s = 4.2 \, J/g^{\circ}C$Mass of water,$m = 400 \, g$Change in temperature,$\Delta T = 40^{\circ}C - 20^{\circ}C = 20

Vedclass · Accepted Answer

$1.69 	imes 10^{28}$

Vedclass · Answer

(B) Given:Specific heat of water,$s = 4.2 \, J/g^{\circ}C$Mass of water,$m = 400 \, g$Change in temperature,$\Delta T = 40^{\circ}C - 20^{\circ}C = 20^{\circ}C$Frequency of light,$
u = 3 	imes 10^9 \, Hz$Planck's constant,$h = 6.63 	imes 10^{-34} \, J \cdot s$Step $1$: Calculate the total heat energy $(Q)$ required to heat the water:$Q = m \cdot s \cdot \Delta T$$Q = 400 \, g 	imes 4.2 \, J/g^{\circ}C 	imes 20^{\circ}C = 33600 \, J$Step $2$: Calculate the energy of a single photon $(E_p)$:$E_p = h \cdot 
u$$E_p = 6.63 	imes 10^{-34} \, J \cdot s 	imes 3 	imes 10^9 \, Hz = 19.89 	imes 10^{-25} \, J$Step $3$: Calculate the number of photons $(n)$ required:$n = \frac{Q}{E_p} = \frac{33600}{19.89 	imes 10^{-25}}$$n \approx 1689.29 	imes 10^{25} \approx 1.69 	imes 10^{28}$Thus,the number of photons needed is $1.69 	imes 10^{28}$.

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

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