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Question
Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency ν is used to convert 1 kg of ice at 0°C to water at 0°C. Then, the time T taken for the conversion ______.
- decreases with increasing n, with ν fixed.
- decreases with n fixed, ν increasing.
- remains constant with n and ν changing such that n ν = constant.
- increases when the product n ν increases.
Options
b and d
a, c and d
a and d
a, b and c
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Solution
a, b and c
Explanation:
We know that energy spent to convert ice into water
`E_("absorb")` = mass × latent heat
∴ E = mL = (1000 g) × (80 cal/g)
E = 80000 cal
Energy of photons used = nT × E = nT × hv ....[∵ E = hv]
So, nThv = mL ⇒ T = `(mL)/(nhv)`
∴ `T oo 1/n`, when v is constant.
Thus, time taken for conversion decreases with increasing n with v kept constant.
`T oo 1/v`, when n remains constant.
Thus, time taken for conversion decreases with increasing v with n kept constant.
⇒ `T oo 1/(nv)`
Thus, time taken for conversion decreases with increase in product of nv and T is constant, if nv is constant.
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