420
10 Heat and Matter
what is the wavelength of the most intense radiation under new conditions?
Wien’s constant b = 3 × 10 −3 m K.
10.2.4 Specific Heat and Latent Heat
10.35 The latest heat of fusion of a material is 6 kJ/mol and the heat capacity (C p )
in solid and liquid phases of the material is a linear function of temperature
C p = 30.6 + 0.0103 T , with units J/mol/K. How much heat is required to
increase the temperature of 1 mol of the material from 20 to 200 ◦ C if the
fusion phase transition occurs at 80 ◦ C?
[University of Manchester 2007]
10.36 The variation of the specific heat of a substance is given by the expression
C = A + BT 2 , where A and B are constants and T is Celsius temperature.
Show that the difference between the mean specific heat and the specific heat
at midpoint T /2 is BT 2 /12.
10.37 The temperature of equal masses of three different liquids A, B and C is 12,
18 and 28 ◦ C, respectively. When A and B are mixed the temperature is 16 ◦ C.
When B and C are mixed, it is 23 ◦ C. What would be the temperature when
A and C are mixed?
[Indian Institute of Technology 1976]
10.38 A 3.0 g bullet moving at 120 m/s on striking a 50 g block of wood is arrested
within the block. Calculate the rise of temperature of the bullet if (a) the
block is fixed; (b) the block is free to move. The specific heat of lead is
0.031 cal/g
◦ C.
10.39 Calculate the difference in temperature between the water at the top and bottom of a 25 m high waterfall assuming that 15% of the energy of fall is spent
in heating the water (J = 4.18 J/Cal).
[University of Durham]
10.40 A piece of lead falls from a height of 100 m on to a fixed non-conducting
slab which brings it to rest. Show that its temperature immediately after
the collision is raised by approximately 7.1 K (the specific heat of lead is
30.6 cal/kg 0 ◦ C between 0 and 100 ◦ C).
10.2.5 Thermodynamics
10.41 (a) Define
(i) an isobaric process
(ii) an isochoric process
10 Heat and Matter
what is the wavelength of the most intense radiation under new conditions?
Wien’s constant b = 3 × 10 −3 m K.
10.2.4 Specific Heat and Latent Heat
10.35 The latest heat of fusion of a material is 6 kJ/mol and the heat capacity (C p )
in solid and liquid phases of the material is a linear function of temperature
C p = 30.6 + 0.0103 T , with units J/mol/K. How much heat is required to
increase the temperature of 1 mol of the material from 20 to 200 ◦ C if the
fusion phase transition occurs at 80 ◦ C?
[University of Manchester 2007]
10.36 The variation of the specific heat of a substance is given by the expression
C = A + BT 2 , where A and B are constants and T is Celsius temperature.
Show that the difference between the mean specific heat and the specific heat
at midpoint T /2 is BT 2 /12.
10.37 The temperature of equal masses of three different liquids A, B and C is 12,
18 and 28 ◦ C, respectively. When A and B are mixed the temperature is 16 ◦ C.
When B and C are mixed, it is 23 ◦ C. What would be the temperature when
A and C are mixed?
[Indian Institute of Technology 1976]
10.38 A 3.0 g bullet moving at 120 m/s on striking a 50 g block of wood is arrested
within the block. Calculate the rise of temperature of the bullet if (a) the
block is fixed; (b) the block is free to move. The specific heat of lead is
0.031 cal/g
◦ C.
10.39 Calculate the difference in temperature between the water at the top and bottom of a 25 m high waterfall assuming that 15% of the energy of fall is spent
in heating the water (J = 4.18 J/Cal).
[University of Durham]
10.40 A piece of lead falls from a height of 100 m on to a fixed non-conducting
slab which brings it to rest. Show that its temperature immediately after
the collision is raised by approximately 7.1 K (the specific heat of lead is
30.6 cal/kg 0 ◦ C between 0 and 100 ◦ C).
10.2.5 Thermodynamics
10.41 (a) Define
(i) an isobaric process
(ii) an isochoric process