Heat Transfer
PHXI11:THERMAL PROPERTIES OF MATTER

366393 A composite rod made of three rods of equal length and cross section, as shown in figure. The thermal conductivities of materiales of rods are \({k / 2,5 k}\) and \({k}\), respectively. The end \({A}\) and end \({B}\) are at constant temperture. The effective thermal conductivity of the bar is \({\left(T_{1}>T_{2}\right)}\)
supporting img

1 \({\dfrac{6 k}{13}}\)
2 \({\dfrac{15 k}{16}}\)
3 \({\dfrac{5 k}{16}}\)
4 \({\dfrac{2 k}{13}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366394 Two rods of same length and transfer a given amount of heat in 12 second, when they are joined as shown in figure (1)
But when they are joined as shown in figure(2) then they will transfer same heat in same conditions in
supporting img

1 \({\text{24 }}s\)
2 \({\text{13 }}s\)
3 \({\text{15 }}s\)
4 \({\text{48 }}s\)
PHXI11:THERMAL PROPERTIES OF MATTER

366395 The ends \(Q\) and \(R\) of two thin wires, \(P Q\) and \(RS\), are joined together. Initially each of the wires has a length of \(1m\) at \(10^\circ C\). Now the end \(P\) is maintained at \(10^\circ C\), while the end \(S\) is heated and maintained at \(400^\circ C\). The system is thermally insulted from its surroundings. If the thermal conductivity of wire \(PQ\) is twice that of the wire RS and the coefficient of linear thermal expansion of \(PQ\) is \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\), the change in length of the wire \(P Q\) is

1 \(2.34\;mm\)
2 \(0.78\;mm\)
3 \(0.90\;mm\)
4 \(1.56\;mm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366396 A cylinder \(A\) of a material of thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of inner radius equal to the cylinder. The shell is made of a material of thermal conductivity \(K_{2}\). The two ends of the combined system are maintained at two different temperatures. If the effective thermal conductivity of the system is \(\dfrac{4 K_{1}+5 K_{2}}{9}\), find the ratio of outer radius of the shell to the radius of the cylinder.
supporting img

1 \(5 / 2\)
2 \(5 / 3\)
3 \(3 / 2\)
4 \(2 / 3\)
PHXI11:THERMAL PROPERTIES OF MATTER

366397 Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination in the given units would be:

1 3.43
2 4.43
3 5.43
4 2.43
PHXI11:THERMAL PROPERTIES OF MATTER

366393 A composite rod made of three rods of equal length and cross section, as shown in figure. The thermal conductivities of materiales of rods are \({k / 2,5 k}\) and \({k}\), respectively. The end \({A}\) and end \({B}\) are at constant temperture. The effective thermal conductivity of the bar is \({\left(T_{1}>T_{2}\right)}\)
supporting img

1 \({\dfrac{6 k}{13}}\)
2 \({\dfrac{15 k}{16}}\)
3 \({\dfrac{5 k}{16}}\)
4 \({\dfrac{2 k}{13}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366394 Two rods of same length and transfer a given amount of heat in 12 second, when they are joined as shown in figure (1)
But when they are joined as shown in figure(2) then they will transfer same heat in same conditions in
supporting img

1 \({\text{24 }}s\)
2 \({\text{13 }}s\)
3 \({\text{15 }}s\)
4 \({\text{48 }}s\)
PHXI11:THERMAL PROPERTIES OF MATTER

366395 The ends \(Q\) and \(R\) of two thin wires, \(P Q\) and \(RS\), are joined together. Initially each of the wires has a length of \(1m\) at \(10^\circ C\). Now the end \(P\) is maintained at \(10^\circ C\), while the end \(S\) is heated and maintained at \(400^\circ C\). The system is thermally insulted from its surroundings. If the thermal conductivity of wire \(PQ\) is twice that of the wire RS and the coefficient of linear thermal expansion of \(PQ\) is \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\), the change in length of the wire \(P Q\) is

1 \(2.34\;mm\)
2 \(0.78\;mm\)
3 \(0.90\;mm\)
4 \(1.56\;mm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366396 A cylinder \(A\) of a material of thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of inner radius equal to the cylinder. The shell is made of a material of thermal conductivity \(K_{2}\). The two ends of the combined system are maintained at two different temperatures. If the effective thermal conductivity of the system is \(\dfrac{4 K_{1}+5 K_{2}}{9}\), find the ratio of outer radius of the shell to the radius of the cylinder.
supporting img

1 \(5 / 2\)
2 \(5 / 3\)
3 \(3 / 2\)
4 \(2 / 3\)
PHXI11:THERMAL PROPERTIES OF MATTER

366397 Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination in the given units would be:

1 3.43
2 4.43
3 5.43
4 2.43
PHXI11:THERMAL PROPERTIES OF MATTER

366393 A composite rod made of three rods of equal length and cross section, as shown in figure. The thermal conductivities of materiales of rods are \({k / 2,5 k}\) and \({k}\), respectively. The end \({A}\) and end \({B}\) are at constant temperture. The effective thermal conductivity of the bar is \({\left(T_{1}>T_{2}\right)}\)
supporting img

1 \({\dfrac{6 k}{13}}\)
2 \({\dfrac{15 k}{16}}\)
3 \({\dfrac{5 k}{16}}\)
4 \({\dfrac{2 k}{13}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366394 Two rods of same length and transfer a given amount of heat in 12 second, when they are joined as shown in figure (1)
But when they are joined as shown in figure(2) then they will transfer same heat in same conditions in
supporting img

1 \({\text{24 }}s\)
2 \({\text{13 }}s\)
3 \({\text{15 }}s\)
4 \({\text{48 }}s\)
PHXI11:THERMAL PROPERTIES OF MATTER

366395 The ends \(Q\) and \(R\) of two thin wires, \(P Q\) and \(RS\), are joined together. Initially each of the wires has a length of \(1m\) at \(10^\circ C\). Now the end \(P\) is maintained at \(10^\circ C\), while the end \(S\) is heated and maintained at \(400^\circ C\). The system is thermally insulted from its surroundings. If the thermal conductivity of wire \(PQ\) is twice that of the wire RS and the coefficient of linear thermal expansion of \(PQ\) is \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\), the change in length of the wire \(P Q\) is

1 \(2.34\;mm\)
2 \(0.78\;mm\)
3 \(0.90\;mm\)
4 \(1.56\;mm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366396 A cylinder \(A\) of a material of thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of inner radius equal to the cylinder. The shell is made of a material of thermal conductivity \(K_{2}\). The two ends of the combined system are maintained at two different temperatures. If the effective thermal conductivity of the system is \(\dfrac{4 K_{1}+5 K_{2}}{9}\), find the ratio of outer radius of the shell to the radius of the cylinder.
supporting img

1 \(5 / 2\)
2 \(5 / 3\)
3 \(3 / 2\)
4 \(2 / 3\)
PHXI11:THERMAL PROPERTIES OF MATTER

366397 Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination in the given units would be:

1 3.43
2 4.43
3 5.43
4 2.43
PHXI11:THERMAL PROPERTIES OF MATTER

366393 A composite rod made of three rods of equal length and cross section, as shown in figure. The thermal conductivities of materiales of rods are \({k / 2,5 k}\) and \({k}\), respectively. The end \({A}\) and end \({B}\) are at constant temperture. The effective thermal conductivity of the bar is \({\left(T_{1}>T_{2}\right)}\)
supporting img

1 \({\dfrac{6 k}{13}}\)
2 \({\dfrac{15 k}{16}}\)
3 \({\dfrac{5 k}{16}}\)
4 \({\dfrac{2 k}{13}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366394 Two rods of same length and transfer a given amount of heat in 12 second, when they are joined as shown in figure (1)
But when they are joined as shown in figure(2) then they will transfer same heat in same conditions in
supporting img

1 \({\text{24 }}s\)
2 \({\text{13 }}s\)
3 \({\text{15 }}s\)
4 \({\text{48 }}s\)
PHXI11:THERMAL PROPERTIES OF MATTER

366395 The ends \(Q\) and \(R\) of two thin wires, \(P Q\) and \(RS\), are joined together. Initially each of the wires has a length of \(1m\) at \(10^\circ C\). Now the end \(P\) is maintained at \(10^\circ C\), while the end \(S\) is heated and maintained at \(400^\circ C\). The system is thermally insulted from its surroundings. If the thermal conductivity of wire \(PQ\) is twice that of the wire RS and the coefficient of linear thermal expansion of \(PQ\) is \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\), the change in length of the wire \(P Q\) is

1 \(2.34\;mm\)
2 \(0.78\;mm\)
3 \(0.90\;mm\)
4 \(1.56\;mm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366396 A cylinder \(A\) of a material of thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of inner radius equal to the cylinder. The shell is made of a material of thermal conductivity \(K_{2}\). The two ends of the combined system are maintained at two different temperatures. If the effective thermal conductivity of the system is \(\dfrac{4 K_{1}+5 K_{2}}{9}\), find the ratio of outer radius of the shell to the radius of the cylinder.
supporting img

1 \(5 / 2\)
2 \(5 / 3\)
3 \(3 / 2\)
4 \(2 / 3\)
PHXI11:THERMAL PROPERTIES OF MATTER

366397 Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination in the given units would be:

1 3.43
2 4.43
3 5.43
4 2.43
PHXI11:THERMAL PROPERTIES OF MATTER

366393 A composite rod made of three rods of equal length and cross section, as shown in figure. The thermal conductivities of materiales of rods are \({k / 2,5 k}\) and \({k}\), respectively. The end \({A}\) and end \({B}\) are at constant temperture. The effective thermal conductivity of the bar is \({\left(T_{1}>T_{2}\right)}\)
supporting img

1 \({\dfrac{6 k}{13}}\)
2 \({\dfrac{15 k}{16}}\)
3 \({\dfrac{5 k}{16}}\)
4 \({\dfrac{2 k}{13}}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366394 Two rods of same length and transfer a given amount of heat in 12 second, when they are joined as shown in figure (1)
But when they are joined as shown in figure(2) then they will transfer same heat in same conditions in
supporting img

1 \({\text{24 }}s\)
2 \({\text{13 }}s\)
3 \({\text{15 }}s\)
4 \({\text{48 }}s\)
PHXI11:THERMAL PROPERTIES OF MATTER

366395 The ends \(Q\) and \(R\) of two thin wires, \(P Q\) and \(RS\), are joined together. Initially each of the wires has a length of \(1m\) at \(10^\circ C\). Now the end \(P\) is maintained at \(10^\circ C\), while the end \(S\) is heated and maintained at \(400^\circ C\). The system is thermally insulted from its surroundings. If the thermal conductivity of wire \(PQ\) is twice that of the wire RS and the coefficient of linear thermal expansion of \(PQ\) is \(1.2 \times {10^{ - 5}}\;{K^{ - 1}}\), the change in length of the wire \(P Q\) is

1 \(2.34\;mm\)
2 \(0.78\;mm\)
3 \(0.90\;mm\)
4 \(1.56\;mm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366396 A cylinder \(A\) of a material of thermal conductivity \(K_{1}\) is surrounded by a cylindrical shell of inner radius equal to the cylinder. The shell is made of a material of thermal conductivity \(K_{2}\). The two ends of the combined system are maintained at two different temperatures. If the effective thermal conductivity of the system is \(\dfrac{4 K_{1}+5 K_{2}}{9}\), find the ratio of outer radius of the shell to the radius of the cylinder.
supporting img

1 \(5 / 2\)
2 \(5 / 3\)
3 \(3 / 2\)
4 \(2 / 3\)
PHXI11:THERMAL PROPERTIES OF MATTER

366397 Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination in the given units would be:

1 3.43
2 4.43
3 5.43
4 2.43