Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice

The coefficient of thermal expansion of a rod is temperature-dependent and is given by the formula α = a T , where a is 3.465 × 10 - 5 ° C - 2 and T in o C . If the length of the rod is l at temperature 0 o C , then the temperature at which the length will be 2 l is [Given, ln 2 = 0 . 693 ]

Options

  1. A12 o C
  2. B20 o C
  3. C200 o C
  4. D100 o C

Correct answer

C. 200 o C

Step-by-step solution

As; d l = α l d T ∴ ∫ l 2 l d l l = a ∫ 0 T T d T ln 2 = a T 2 2 ∴ T = ln 4 a 1 2 = 2 × 0.693 3.465 × 10 - 5 1 2 = 2 5 × 10 5 = 200 o C

Practice Thermal Properties of Matter on Quantrex Academy →

More from Thermal Properties of Matter

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition (P₁) and a freely movable but thermally insulated piston (P₂) . The par 2026The heat extracted out of x gram of water initially at 50°C to cool it down to 0°C is sufficient to evaporate (1000 - x) gram of water also initially at 50°C . The value of x (clos 2026The temperature of a metal strip having coefficient of linear expansion is increased from T₁ to T₂ resulting in increase of its length by L₁ . The temperature is further increased 2026Which of the following best represents the temperature versus heat supplied graph for water, in the range of -20^ C to 120^ C ? 202610 kg of ice at -10^ C is added to 100 kg of water to lower its temperature from 25 ^ C . Consider no heat exchange to surroundings. The decrement to the temperature of water is _ 2026A brass wire of length 2 m and radius 1 mm at 27^ C is held taut between two rigid supports. Initially it was cooled to a temperature of -43^ C creating a tension T in the wire. Th 2026Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100^ C and 40^ C respectively. Given 2026An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30^ C . The coefficient of linear expansion of aluminium and steel a 2026 Full Thermal Properties of Matter list All NTA Abhyas JEE Main PYQs