Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202520 Apr 2025Evening ShiftPhysicsThermal Properties of MatterActual

A metal sphere cools at a rate of 1.5^ C / min when its temperature is 80^ C . When the temperature of the sphere is 40^ C , its rate of cooling is 0.3^ C / min . The temperature of the surrounding ( ₀ ) is

Options

  1. A30^ C
  2. B35^ C
  3. C25^ C
  4. D27^ C

Correct answer

A. 30^ C

Step-by-step solution

According to Newton's Law of Cooling, the rate of cooling is proportional to the temperature difference: d dt = -K( - ₀) Given two measurements: At ₁ = 80^ C, cooling rate is 1.5^ C/min At ₂ = 40^ C, cooling rate is 0.3^ C/min Dividing the corresponding equations: 1.5 0.3 = 80 - ₀ 40 - ₀ Solving for ₀ : 5(40 - ₀) = 80 - ₀ 200 - 5 ₀ = 80 - ₀ 120 = 4 ₀ ₀ = 30^ C The surrounding temperature is therefore 30^ C. Final answer: A

Practice Thermal Properties of Matter on Quantrex Academy →

More from Thermal Properties of Matter

A block of a certain material is heated to a temperature of 500° C and then placed on a large ice block. If 1.455 kg of ice melts, find the mass of the block. Specific heat of the 2026Two bodies of specific heats C₁ and C₂ , having the same heat capacities are combined to form a single composite body. The specific heat capacity of the composite body is 2026A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio 4: 1 . If the free face of brass is at 0 ^ C and that of copp 2025If some heat is given to a metal of mass 100 g, its temperature rises by 20^ C . If the same heat is given to 20 g of water, the change in its temperature (in ^ C ) is (The ratio o 2025If a body cools from a temperature of 62^ C to 50^ C in 10 minutes and to 42^ C in the next 10 minutes, then the temperature of the surroundings is 2025The temperature of water of mass 100 g is rasied from 24^ C to 90^ C by adding steam to it. The mass of the steam added is (Latent heat of steam =540 cal g ⁻¹ and specific heat cap 2025Steam at 100^ C is passed into 114 g of water at 30^ C . The mass of water present in the mixture when the temperature of the water becomes 70^ C is (Latent heat of steam =540 cal 2025A small quantity of water of mass ' m ' at temperature ^ C is mixed with a large mass ' M ' of ice which is at its melting point. If ' s ' is specific heat capacity of water and ' 2025 Full Thermal Properties of Matter list All MHT CET PYQs