## Question

A slab of stone of area 0.34 m^{2} and thickness 10 cm is exposed on the lower face to steam at 100^{o}C. A block of ice at 0^{o}C rests on the upper face of the slab. In one hour, 3.6 kg of ice is melted. Assume that the heat loss from the sides is negligible. The latent heat of fusion of ice is What is the thermal conductivity of the stone in units of Js^{–1}m^{–1o}C^{–1}?

### Solution

1.0

Amount of heat flowing through the stone in 1 hour = *m*L, where *m* is the mass of ice melted and *L *its latent heat. Now time (*t*) = 1 hour = 3600 s and thickness *d = *10 cm = 0.1 m. The rate of flow of heat is

#### SIMILAR QUESTIONS

A copper block of mass 2 kg is heated to a temperature of 500^{o}C and then placed in a large block of ice at 0^{o}C. What is the maximum amount of ice that can melt? The specific heat of copper is 400 j and latent heat of fusion of water is .

The dimensions of the coefficient of thermal conductivity are

Two different metal rods of the same length have their ends kept at the same temperatures and with . If *A* and *B *are their cross-sectional areas and *k*_{1} and *k*_{2} their thermal conductivities, the rate of flow of heat in the two rods will be the same if

Two rods *A* and *B* of different materials are welded together as shown in Fig. If their thermal conductivities are *k*_{1} and *k*_{2} , the thermal conductivity of the composite rod will be

A one liter flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in the flask? Given the coefficient of linear expansion of glass ^{o}C^{–1}, the coefficient of volume expansion of mercury is ^{o}C^{–1}.

A wire of cross-sectional area *A* at temperature *t* is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature what tension is developed in the wire? The coefficient of linear expansion is and the Young’s modulus of the wire is *Y*.

Two uniform brass rods *A* and *B *of length *l* and 2*l *and radii 2*r* and *r*respectively are heated to the same temperature. The ratio of the increase in the length of *A* to that of *B* is

Two rods of different materials having coefficients of thermal expansion and Young’s modulii *Y*_{1}, *Y*_{2} respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If the thermal stresses developed in the two rods are equal provided *Y*_{1} : *Y*_{2} is equal to:

The water equivalent of a copper calorimeter is 4.5 g. If the specific heat of copper is 0.09 cal.g^{–1o}C^{–1} the

An ice-box is made of wood 1.75 cm thick, lined inside with cork 2 cm thick. If the temperature of the inner surface of the cork is steady at 0^{o}C and that of the outer surface is steady at 12^{o}C, what is the temperature of the surface? The thermal conductivity of wood is 5 times that of cork.