Heat transfer: conduction, convection, radiation
- Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature… Answer: 3. 5/3 Key idea: in steady state the same heat current flows through all three rods, so kA Δ T/l is equal for each. With equal A and... 1
- A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is : Answer: 2. 13/5t Key idea: Newton's law of cooling in the average-temperature form: Δ T/t=k(T_avg-T₀) . First case: 10/t=k(85-20)=65k⇒ k=2/1... 1
- The unit of thermal conductivity is : Answer: 4. W m ⁻¹ K ⁻¹ From Q/T=KA Δθ/L , K=(Q/t) L/A Δθ . Unit of Q/t is W, L is m, A is m ² , Δθ is K. So K has unit W m/m² K=W m⁻¹K⁻¹ . 1
- The power radiated by a black body is P and it radiates maximum energy at wavelength, λ_0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 34λ_0, the power radiated by it becomes nP. The value of n… Answer: 2. 256/81 Wien's law: λ_mT= constant, so T∝dfrac1λ_m . Stefan's law: P∝ T⁴ . New wavelength is 3/4λ₀ , so T'=4/3T . n=(4/3)⁴=256/81 1
- A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be : Answer: 3. 1800 Key idea: power radiated P=σ AT⁴∝ r²T⁴ . Radius halved gives factor 1/4 ; temperature doubled gives factor 2⁴=16 . P'=450×1/... 1
- Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_1 and K_2. The thermal conductivity of the composite rod will be : Answer: 4. K₁+K₂/2 Key idea: the two rods are side by side, so heat flows through them in parallel, and the conductances add. Let each rod h... 1
- A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be Answer: 1. 3/2T Use Newton's law in the average form: rate of fall =k (mean temperature-T) . First 10 min: 3T-2T/10=k(3T+2T/2-T)=k·3/2T , so... 1
- A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U_1, at wavelength 500 nm is U_2 and that at 1000 nm is U_3. Wien's constant, b = 2.88×10^6 nmK. Which of the following is correct ? Answer: 4. U₂ > U₁ Key idea: Wien's law λ_m T=b gives the wavelength of peak emission. λ_m=dfrac2.88×10⁶5760=500 nm. Emission is maximum at... 1