Question

A hollow, iron sphere of inner radius 16 cm, outer radius 24 cm, and emissivity 0.45 has a 750 gram block of ice at 0◦C suspended at its center with a small drip pan underneath it.

(a) What must the temperature of the inside surface of the sphere be for the ice to completely melt in 35 seconds?

(b) What must the temperature at the outer surface of the sphere be for the inside temperature to be maintained during the process?

Answer #1

part a:

let temperature of the inside surface be T K. (T>273 K, where 273 K is melting point of ice)

then heat received by ice per second=emissivity*steffan's constant*area *(T^4-273^4)

=0.45*5.67*10^(-8)*pi*0.16^2*(T^4-273^4)

given that ice melts in 35 seconds.

energy required=mass*latent heat of fusion

=0.75*336 kJ=252 kJ

then 252*1000=0.45*5.67*10^(-8)*pi*0.16^2*(T^4-273^4)*35

==>T^4-273^4=3.5087*10^12

==>T=1369.1736 K=1096.1736 degree celcius

part b:

thermal conductivity of iron=79.5 W/(m.K)

area of the iron portion =pi*(0.24^2-0.16^2)=0.110531 m^2

if outer temperature is T degree celcius,

then heat transmitted through thermal conduction=heat being provided to ice

==>79.5*0.100531*(T-1096.1736)/0.08=0.45*5.67*10^(-8)*pi*0.16^2*(1369.1736^4-273^4)

==>T=1168.2437 degree celcius

A hollow, conducting sphere with an outer radius of 0.260 m and
an inner radius of 0.200 m has a uniform surface charge density of
+6.47 × 10−6 C/m2. A charge of -0.400 μC is now introduced into the
cavity inside the sphere.
a)What is the new charge density on the outside of the
sphere?
b)Calculate the strength of the electric field just outside the
sphere
c)What is the electric flux through a spherical surface just
inside the inner surface...

A hollow, conducting sphere with an outer radius of 0.260 mm and
an inner radius of 0.200 mm has a uniform surface charge density of
+6.57 ×× 10−6−6 C/m2C/m2. A charge of -0.700 μCμC is now introduced
into the cavity inside the sphere.
What is the new charge density on the outside of the sphere?
Calculate the strength of the electric field just outside the
sphere.
What is the electric flux through a spherical surface just
inside the inner surface...

A hollow, conducting sphere with an outer radius of 0.260 m and
an inner radius of 0.200 m has a uniform surface charge density of
+6.37 × 10−6 C/m2. A charge of -0.700 μC is now introduced into the
cavity inside the sphere. a) What is the new charge density on the
outside of the sphere? b) Calculate the strength of the electric
field just outside the sphere. c) What is the electric flux through
a spherical surface just inside...

A hollow, conducting sphere with
an outer radius of 0.260m and an inner radius of 0.207m has a
uniform surface charge density of +6.79

A hollow metal sphere has inner radius a, outer radius b, and
conductivity σ. The current I is radially outward from the inner
surface to the outer surface. Part APart complete Find an
expression for the electric field strength inside the metal as a
function of the radius r from the center. Express your answer in
terms of the variables I, σ, r, and appropriate constants. E =
Iσ(4πr2) Previous Answers Correct Part B Evaluate the electric
field strength at...

Consider an insulating sphere of radius 5 cm surrounded by a
conducting sphere of inner radius 22 cm and outer radius 25 cm.
Furthermore, suppose that the electric field at a point 13 cm from
the center is measured to be 1540 N/C radially inward while the
electric field at a point 44 cm from the center is 90 N/C radially
outward.
1. Find the charge on the insulating sphere. Answer in units of
C.
2.Find the net charge on...

A hollow sphere of inner radius 5.1 cm and outer radius
7.0 cm floats half submerged in a liquid of density 640
kg/m3. What is the mass of the
sphere?
(in kg)
A: 4.60×10-1
B: 6.11×10-1
C: 8.13×10-1
D: 1.08
E: 1.44
calculate the density of the material of which
the sphere is made.
(in kg/m^3)
A: 5.22×102
B: 7.57×102
C: 1.10×103
D: 1.59×103
E: 2.31×103

A hollow metal sphere has 5cm and 10cm inner and outer radii,
respectively. The surface charge density on the inside surface is
?150nC/m2 . The surface charge density on the exterior surface is
+150nC/m2 .
What is the strength of the electric field at point 12 cm from
the center?

A neutral hollow spherical conducting shell of inner radius 1.00
cm and outer radius 3.00 cm has a +2.00-µC point charge placed at
its center. Find the surface charge density how does the magnitude
of the charge and radius relate? How does a -2.00µC get involved in
this problem?

The emissivity of tungsten is 0.350. A tungsten sphere with a
radius of 1.75 cm is suspended within a large evacuated enclosure
whose walls are at 315 K. What power input is required to maintain
the sphere at a temperature of 3000K if heat conduction along the
supports is negligible?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 18 minutes ago

asked 19 minutes ago

asked 20 minutes ago

asked 36 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago