Photons absorbed in matter are converted to heat. A source emitting n photons/ sec of frequency `nu` is used to convert 1kg of ice at `0^(@)C` to water at `0^(@)C`. Then, the time T taken for the conversion

Options

A. decreases with increasing n, with v fixed.
B. decreases with n fixed , v increasing.
C. remains constant with n and v changing such that nv = constant.
D. increases when the product nv increases.

Answer

A, B, C

Explanation

Latent heat of fusion of ice L = 80 cal/g
Mass of ice , m = 100 g
Energy required to convert ice into water is
H = mL = `100 g xx 80 ` cal/g = 80, 000 cal
Energy of each photon , E = hv
Given , time taken for conversion = T
Energy of photons used `=nT xxE = nT xxhv`
Then, nT hv = mL
`implies T = (mL)/(nhv)`
`:.` If v is constant , `T prop 1//n`
Also , if both n and v are varying , `T prop 1 n//v`
If the value of nv is constant , T is constant.