Question

Photons absorbed in matter are converted to heat. A source emitting n photons per second of frequency $\upsilon$ is used to convert $1 \,kg$ of ice at $0^{\circ}C$ to water at $0^{\circ}C$ Then, the time $T$ taken for the conversion

• A. decreases with increasing $n$, with $\upsilon$ fixed
• B. decreases with $n$ fixed, $\upsilon$ increasing
• C. remains constant with $n$ and $\upsilon$ changing such that $n\upsilon$ = constant
• D. All of these

Answer 1

Answer: (D)

Energy spent to convert ice into water
$=mL=\left(1000\,g\right)\times80\,cal\,g^{-1}=80000\, cal$
Energy of photons used $=nT\times E=nT\times h\upsilon$
$\therefore nTh\upsilon=mL$ or $T=\frac{mL}{nh\upsilon}$
$\therefore T \propto1/ n$ when $\upsilon$ is constant , $T \propto1/ \upsilon $ when $n$ fixed, $T \propto1 /n\upsilon $ Thus $T$ is constant if $n\upsilon$ is constant.