Heat Transfer
PHXI11:THERMAL PROPERTIES OF MATTER

366428 Which of the following circular rods, (given radius \(r\) and lenght \(l\)) each made of the same material and whose ends are maintained at the same temperature will conduct more heat?

1 \(r=2 r_{0}, l=2 l_{0}\)
2 \(r=2 r_{0}, l=l_{0}\)
3 \(r=r_{0}, l=l_{0}\)
4 \(r=r_{0}, l=2 l_{0}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366429 Two identical vessels are filled with equal amounts of ice. The vessels are made from different materials. If the ice melts in the two vessels are in times \(t_{1}\) and \(t_{2}\) respectively then their thermal conductivities are in the ratio

1 \(t_{2}^{2}: t_{1}^{2}\)
2 \(t_{2}: t_{1}\)
3 \(t_{1}: t_{2}\)
4 \(t_{1}^{2}: t_{2}^{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366430 A hollow spherical ball of inner radius \(a\) and outer radius \(2 a\) is made of a uniform material of constant thermal conductivity \(K\). The temperature within the ball is maintained at \(2 T_{0}\) and outside the ball is \(T_{0}\). Find the temperature at \(r = \frac{{3a}}{2}\)
supporting img

1 \(\dfrac{7 T_{0}}{5}\)
2 \(\dfrac{4 T_{0}}{3}\)
3 \(\dfrac{5 T_{0}}{3}\)
4 \(\dfrac{3 T_{0}}{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366431 A rod of length \(l\) and cross-sectional area \(A\) has a variable conductivity given by \(K=\alpha T\) where \(\alpha\) is a positive constant and \(T\) is temperature in kelvin. Two ends of the rod are maintained at temperatures \(T_{1}\) and \(T_{2}\left(T_{1}>T_{2}\right)\). Heat current flowing through the rod will be

1 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{3 l}\)
2 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{2 l}\)
3 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{6 l}\)
4 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{l}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366428 Which of the following circular rods, (given radius \(r\) and lenght \(l\)) each made of the same material and whose ends are maintained at the same temperature will conduct more heat?

1 \(r=2 r_{0}, l=2 l_{0}\)
2 \(r=2 r_{0}, l=l_{0}\)
3 \(r=r_{0}, l=l_{0}\)
4 \(r=r_{0}, l=2 l_{0}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366429 Two identical vessels are filled with equal amounts of ice. The vessels are made from different materials. If the ice melts in the two vessels are in times \(t_{1}\) and \(t_{2}\) respectively then their thermal conductivities are in the ratio

1 \(t_{2}^{2}: t_{1}^{2}\)
2 \(t_{2}: t_{1}\)
3 \(t_{1}: t_{2}\)
4 \(t_{1}^{2}: t_{2}^{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366430 A hollow spherical ball of inner radius \(a\) and outer radius \(2 a\) is made of a uniform material of constant thermal conductivity \(K\). The temperature within the ball is maintained at \(2 T_{0}\) and outside the ball is \(T_{0}\). Find the temperature at \(r = \frac{{3a}}{2}\)
supporting img

1 \(\dfrac{7 T_{0}}{5}\)
2 \(\dfrac{4 T_{0}}{3}\)
3 \(\dfrac{5 T_{0}}{3}\)
4 \(\dfrac{3 T_{0}}{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366431 A rod of length \(l\) and cross-sectional area \(A\) has a variable conductivity given by \(K=\alpha T\) where \(\alpha\) is a positive constant and \(T\) is temperature in kelvin. Two ends of the rod are maintained at temperatures \(T_{1}\) and \(T_{2}\left(T_{1}>T_{2}\right)\). Heat current flowing through the rod will be

1 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{3 l}\)
2 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{2 l}\)
3 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{6 l}\)
4 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{l}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366428 Which of the following circular rods, (given radius \(r\) and lenght \(l\)) each made of the same material and whose ends are maintained at the same temperature will conduct more heat?

1 \(r=2 r_{0}, l=2 l_{0}\)
2 \(r=2 r_{0}, l=l_{0}\)
3 \(r=r_{0}, l=l_{0}\)
4 \(r=r_{0}, l=2 l_{0}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366429 Two identical vessels are filled with equal amounts of ice. The vessels are made from different materials. If the ice melts in the two vessels are in times \(t_{1}\) and \(t_{2}\) respectively then their thermal conductivities are in the ratio

1 \(t_{2}^{2}: t_{1}^{2}\)
2 \(t_{2}: t_{1}\)
3 \(t_{1}: t_{2}\)
4 \(t_{1}^{2}: t_{2}^{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366430 A hollow spherical ball of inner radius \(a\) and outer radius \(2 a\) is made of a uniform material of constant thermal conductivity \(K\). The temperature within the ball is maintained at \(2 T_{0}\) and outside the ball is \(T_{0}\). Find the temperature at \(r = \frac{{3a}}{2}\)
supporting img

1 \(\dfrac{7 T_{0}}{5}\)
2 \(\dfrac{4 T_{0}}{3}\)
3 \(\dfrac{5 T_{0}}{3}\)
4 \(\dfrac{3 T_{0}}{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366431 A rod of length \(l\) and cross-sectional area \(A\) has a variable conductivity given by \(K=\alpha T\) where \(\alpha\) is a positive constant and \(T\) is temperature in kelvin. Two ends of the rod are maintained at temperatures \(T_{1}\) and \(T_{2}\left(T_{1}>T_{2}\right)\). Heat current flowing through the rod will be

1 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{3 l}\)
2 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{2 l}\)
3 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{6 l}\)
4 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{l}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366428 Which of the following circular rods, (given radius \(r\) and lenght \(l\)) each made of the same material and whose ends are maintained at the same temperature will conduct more heat?

1 \(r=2 r_{0}, l=2 l_{0}\)
2 \(r=2 r_{0}, l=l_{0}\)
3 \(r=r_{0}, l=l_{0}\)
4 \(r=r_{0}, l=2 l_{0}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366429 Two identical vessels are filled with equal amounts of ice. The vessels are made from different materials. If the ice melts in the two vessels are in times \(t_{1}\) and \(t_{2}\) respectively then their thermal conductivities are in the ratio

1 \(t_{2}^{2}: t_{1}^{2}\)
2 \(t_{2}: t_{1}\)
3 \(t_{1}: t_{2}\)
4 \(t_{1}^{2}: t_{2}^{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366430 A hollow spherical ball of inner radius \(a\) and outer radius \(2 a\) is made of a uniform material of constant thermal conductivity \(K\). The temperature within the ball is maintained at \(2 T_{0}\) and outside the ball is \(T_{0}\). Find the temperature at \(r = \frac{{3a}}{2}\)
supporting img

1 \(\dfrac{7 T_{0}}{5}\)
2 \(\dfrac{4 T_{0}}{3}\)
3 \(\dfrac{5 T_{0}}{3}\)
4 \(\dfrac{3 T_{0}}{2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366431 A rod of length \(l\) and cross-sectional area \(A\) has a variable conductivity given by \(K=\alpha T\) where \(\alpha\) is a positive constant and \(T\) is temperature in kelvin. Two ends of the rod are maintained at temperatures \(T_{1}\) and \(T_{2}\left(T_{1}>T_{2}\right)\). Heat current flowing through the rod will be

1 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{3 l}\)
2 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{2 l}\)
3 \(\dfrac{A \alpha\left(T_{1}^{2}-T_{2}^{2}\right)}{6 l}\)
4 \(\dfrac{A \alpha\left(T_{1}^{2}+T_{2}^{2}\right)}{l}\)