Two copper spheres of radii $6 c m$ and $12 c m$ respectively are suspended in an evacuated enclosure. Each of them are at a temperature $15^{0} C$ above the surroundings. The ratio of their rate of loss of heat is ___________.

2 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 : 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8 : 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $1 : 4$
According to the Stefan-Boltzmann law, the rate of loss of heat from a hot body is given as
$P = σ A (T^{4} - T_{c}^{4})$
$= σ 4 π r^{2} (T^{4} - T_{c}^{4})$
Hence $\frac{P_{1}}{P_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}}$
$= \frac{6^{2}}{12^{2}}$
$= \frac{1}{4}$

Suggest Corrections

Similar questions

Q. Two hot copper spheres of radii in the ratio

2 : 3

are kept in an evacuated enclosure. If each sphere is initially at a temperature

10

^{o}

C above that of the enclosure, the rates of loss of heat of the spheres will be in the ratio of

Q. The emissivity of tungsten is approximately

0.35

. A tungsten sphere

1 cm

in radius is suspended within a large evacuated enclosure whose walls are at

300 K

. Find power input required to maintain the sphere at a temperature of

3000 K

, if heat conduction along the supports is neglected?

σ = 5.67 \times 10^{- 8} SI units

Two spheres of same radius $R$ have their densities in the ratio $8 : 1$ and the ratio of their specific heats are $1 : 4$ . If by radiation their rates of fall of temperature are same, then find the ratio of their rates of losing heat.

Q. If the radii of the two copper sphere are in the ration

1 : 3

and their temperatures are in the ratio

9 : 1

then the ratio of the heat contents in them will be

Q. A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identically surrounding temperatures. Assume that the emissivity of both the spheres in the same. Find the ratio of (a) the rate of heat loss from the aluminium sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminium sphere to the rate of fall of temperature of the copper sphere. The specific heat capacity of aluminium = 900 J kg⁻¹°C⁻¹ and that of copper = 390 J kg⁻¹°C⁻¹. The density of copper = 3.4 times the density of aluminium.

Join BYJU'S Learning Program

Two copper spheres of radii 6cm and 12cm respectively are suspended in an evacuated enclosure. Each of them are at a temperature 150C above the surroundings. The ratio of their rate of loss of heat is ___________.

The correct option is C 1:4According to the Stefan-Boltzmann law, the rate of loss of heat from a hot body is given as P=σA(T4−T4c)=σ4πr2(T4−T4c)Hence P1P2=r21r22=62122=14

Two copper spheres of radii $6 c m$ and $12 c m$ respectively are suspended in an evacuated enclosure. Each of them are at a temperature $15^{0} C$ above the surroundings. The ratio of their rate of loss of heat is ___________.

The correct option is C $1 : 4$
According to the Stefan-Boltzmann law, the rate of loss of heat from a hot body is given as
$P = σ A (T^{4} - T_{c}^{4})$
$= σ 4 π r^{2} (T^{4} - T_{c}^{4})$
Hence $\frac{P_{1}}{P_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}}$
$= \frac{6^{2}}{12^{2}}$
$= \frac{1}{4}$