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Standard XII

Chemistry

Rate Constant

If the temper...

Question

If the temperature of the Sun were to increase from $T$ to $2 T$ and its radius from $R$ to $2 R$ , then the ratio of the radiant energy received on Earth to what it previously was, will be :

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Solution

The correct option is D 64
Energy transfer rate is proportional to area and fourth power of temperature.
Therefore,
$E \propto A T^{4}$
$\frac{E_{1}}{E_{2}}$ $= \frac{A_{1}}{A_{2}}$ ${(\frac{T_{1}}{T_{2}})}^{4}$ $= \frac{R^{2} T^{4}}{(2 R)^{2} (2 T)^{4}}$ = $\frac{1}{64}$
$E_{2}$ $= 64 E_{1}$

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If the temperature of the Sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on Earth to what it previously was, will be :

The correct option is D 64Energy transfer rate is proportional to area and fourth power of temperature. Therefore,E∝AT4E1E2 =A1A2 (T1T2)4 =R2T4(2R)2(2T)4 = 164E2 =64E1

If the temperature of the Sun were to increase from $T$ to $2 T$ and its radius from $R$ to $2 R$ , then the ratio of the radiant energy received on Earth to what it previously was, will be :

The correct option is D 64
Energy transfer rate is proportional to area and fourth power of temperature.
Therefore,
$E \propto A T^{4}$
$\frac{E_{1}}{E_{2}}$ $= \frac{A_{1}}{A_{2}}$ ${(\frac{T_{1}}{T_{2}})}^{4}$ $= \frac{R^{2} T^{4}}{(2 R)^{2} (2 T)^{4}}$ = $\frac{1}{64}$
$E_{2}$ $= 64 E_{1}$