CONTENT:

Specific heat:

• It is defined as theamount of heat required to increase the temperature by 1°Kfor 1 kgof material.

⇒Q = mC∆t -----(1)

Where Q(J) = quantity of heat absorbed by a body, m(kg) = mass of the body, ∆t(°K) = Rise in temperature, and C = Specific heat

• S.I unitof specific heat ist isJ kg-1K-1.

Photon:

• According to Einstein's theory,the light propagates in the bundles of energy, each bundle is being called aphoton.
• ​Therest mass of the photon is zero. But its effective mass is given as,
• Photonexerts pressure on the surface.

• The energy of a photon is given as,

⇒ E = hν

Where, h = Planck's constant, and ν= frequency

CALCULATION:

Given (Specific heat) C= 4.2J/gº-C, (mass) m = 500 g, T1= 30° C,T2= 50° C, and(frequency) ν =2×109 Hz

• We know that the energy of one photon is given as (h = 6.6×10-34J-sec),

⇒ E = hν

⇒ E =6.6 × 10-34× 2 × 109

⇒ E = 13.2 × 10-25J -----(1)

• The change in temperature of the water is given as,

⇒ΔT =T2- T1

⇒ΔT = 50 - 30

⇒ΔT = 20°C

• The heat needed for 20°C temperature change for 500 gm of water is given as,

⇒ Q = mCΔT

⇒ Q = 500 × 4.2 × 20

⇒ Q = 42000 J -----(2)

• If N number of the photon is required to change this temperature, then,

⇒ NE = Q

\(⇒ N=\frac{42000}{13.2×10^{-25}}\)

⇒ N =3.2 × 1028

• Hence, option 2 is correct.