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Thermal Properties of Matter · Question 13

JEE Main 2025 (Online) 7th April Evening ShiftNumericalMedium📈 Topic in 6% papers+4
1

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivities of these rods are: LALB = 12, rArB = 2 and KAKB = 12. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is K, when equilibrium is established.

Answer

360

Solution

Thermal resistance of a rod: Rth = LKA, with A = r2

AAAB = ( rArB )2 = 4

RARB = LALB KBKA ABAA = 12 2 14 = 14

In the steady state the same heat current flows through both rods (interface temperature T):

400 - TRA = T - 200RB

4(400 - T) = T - 200

5T = 1800

T = 360 K

Answer: 360

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2

Consider a rectangular sheet of solid material of length l = 9 cm and width d = 4 cm. The coefficient of linear expansion is = 3.1 10-5 K-1 at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity Cv = 900 J kg-1 K-1. If the amount of heat supplied to the material is 8.1 102 J then change in area of the rectangular sheet is :

  1. 2.0 10-6 m2
  2. 6.0 10-7 m2
  3. 3.0 10-7 m2
  4. 4.0 10-7 m2
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3

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4\% when heated by 1 . Its initial temperature must be:

  1. 2500 K
  2. 25
  3. 250
  4. 250 K
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4

Match List - I with List - II. Choose the correct answer from the options given below :

  1. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
  2. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
  3. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
  4. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
JEE Main 2025 (Online) 2nd April Evening Shift

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