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⚛️ NEET Physics❓ Question

Stefan's law with Celsius temperatures, Wien's displacement direction, and why the average-temperature trick works in Newton's cooling

Kabir Joshi11th Sample

20 Aug 2026 · 1 min read

Three doubts from the same chapter and my notes are inconsistent.

1. A body at 27°C is heated to 327°C. By what factor does the power it radiates (Stefan's law) increase? I did (327/27)4≈21,000(327/27)^4 \approx 21{,}000 and it's nowhere in the options.

2. Wien's law is λmT=b\lambda_m T = b where b≈2.9×10−3b \approx 2.9\times10^{-3} m K. I know the formula but not the direction: when a body gets hotter, does the peak wavelength go up or down? How do I connect this to the colour of a hot iron rod?

3. Newton's law of cooling: a body cools from 80°C to 60°C in 5 min, with surroundings at 20°C. How long to cool from 60°C to 50°C? I used

T1−T2t=k(T1+T22−T0)\frac{T_1 - T_2}{t} = k\left(\frac{T_1+T_2}{2} - T_0\right)

and got about 3.57 min. Why can I use the average temperature when the real law is exponential? And is Newton's law valid for big temperature differences?

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  • [+]Aman YadavDropperSample· 2mo ago

    Stefan's law has absolute temperature, so convert. T1=27+273=300T_1 = 27 + 273 = 300 K, T2=327+273=600T_2 = 327 + 273 = 600 K.

    P2P1=(600300)4=24=16\frac{P_2}{P_1} = \left(\frac{600}{300}\right)^4 = 2^4 = 16

    Never put Celsius in T4T^4. Power goes up 16 times.

    • [+]Kabir Joshi11thSample· 2mo agoAuthor

      ohh, the 16 times. made the Celsius mistake in the second question too. will rewrite my notes in Kelvin

  • [+]Dev Agarwal12thSample· 2mo ago

    Constants to remember: Stefan–Boltzmann constant σ=5.67×10−8\sigma = 5.67\times10^{-8} W m⁻² K⁻⁴, so a black body radiates σT4\sigma T^4 per unit area. A real surface radiates eσT4e\sigma T^4 with emissivity ee between 0 and 1. Two things happen when a body gets hotter: total radiation goes up as T4T^4, and the peak moves to shorter wavelength (Wien). Blue stars are hotter than red stars.

  • [+]Tanvi Deshmukh12thSample· 2mo ago

    For your Q2, Kabir, the direction is λm∝1/T\lambda_m \propto 1/T. Hotter means the peak shifts to shorter wavelength. That's why a heated iron rod first glows dull red (peak is in the infrared, the visible tail is red), then orange, then yellow-white as it gets hotter; the peak shifts toward the visible and the blue side grows.

    Example: if a star's emission peaks near 500 nm,

    T=bλm=2.9×10−35×10−7=5800 KT = \frac{b}{\lambda_m} = \frac{2.9\times10^{-3}}{5\times10^{-7}} = 5800\ \text{K}

    which is about the Sun's surface temperature. Higher T, smaller λm\lambda_m.

    • [+]Dev Agarwal12thSample· 2mo ago

      so blue = hot, red = cooler, and shorter wavelength for hotter. that's how i'll remember wien's direction 🙏

  • [+]Farhan ShaikhDropperSample· 2mo ago

    Your 3.57 min matches the "exact" exponential answer, which is about 3.55 min. Here's the reason. Newton's law says dT/dt=−k(T−T0)dT/dt = -k(T - T_0), so the exact solution is T−T0=(Ti−T0)e−ktT - T_0 = (T_i - T_0)e^{-kt}. Over a small drop (80 to 60) the exponential curve is almost a straight line, so "average rate = rate at the average temperature" is a very good approximation. The error is small for narrow ranges, which is why NCERT/books use it.

    Newton's law itself is only valid for small temperature differences between the body and surroundings. For large differences, radiation (the T4T^4 law) dominates and cooling isn't exponential anymore.

  • [+]Harsh Gupta12thSample· 2mo ago

    Also remember Stefan's law for the net loss: a body at TT in surroundings at T0T_0 gives

    P=σAe (T4−T04)P = \sigma A e\,(T^4 - T_0^4)

    Everything radiates all the time, even cold things. Your hot tea loses heat because it radiates more than it receives. The sofa isn't "cold", it's just radiating about as much as it gets. 😎 And for a perfect black body e=1e = 1.

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