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MHT-CET Physics · Formula sheet

Thermal Properties of Matter formulas

8 formulas, 1 reference table and 14 common traps for MHT-CET Physics Thermal Properties of Matter, grouped by subtopic.

Full notes with worked examples

Temperature Scales and Thermal Expansion

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Converting Between Temperature Scales

Scale conversion

C5=F−329=K−2735\frac{C}{5} = \frac{F - 32}{9} = \frac{K - 273}{5}

Linear Expansion and Rods That Keep Their Difference

Linear expansion

ΔL=αLΔT\Delta L = \alpha L \Delta T

Area and Volume Expansion

Area and volume

ΔA=2αA ΔT,ΔV=3αV ΔT\Delta A = 2\alpha A\,\Delta T, \qquad \Delta V = 3\alpha V\,\Delta T

Common traps

Forgetting the 32 in Fahrenheit

Fahrenheit is not a scaled Celsius: it starts at 32. Subtract 32 before multiplying by 5/9, not after.

Pairing the longer rod with the larger α

Equal growth needs αL equal, so the longer rod has the SMALLER coefficient: L_A/L_B = α_B/α_A, not α_A/α_B.

Using the final length in ΔL = αLΔT

L is the original length. For the small changes asked here the difference is negligible, but a question that gives length 'at 0 °C' means use that one.

Using α for a volume

A volume grows by 3αVΔT. A percentage change in VOLUME gives γ; dividing by 3 gives α, and the options include γ itself.

Calorimetry: Heat Lost Equals Heat Gained

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Mixing, Melting and Heat From Motion

Heat balance

m1c1(T1−T)=m2c2(T−T2),Q=mLm_1c_1(T_1 - T) = m_2c_2(T - T_2), \qquad Q = mL

Common traps

Averaging temperatures when ice is present

Melting absorbs heat without raising the temperature. 540 g of water at 80 °C gives up exactly the 43 200 cal that 540 g of ice needs to melt, so the mixture ends at 0 °C, not at an average.

Confusing heat capacity with specific heat

Specific heat c is per gram; heat capacity mc is for the whole body. 'Heat that raises the BODY by 1 °C' is heat capacity.

Conduction Through Rods and Slabs

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Rate of Flow and Thermal Resistance

Conduction

Qt=KA ΔTL=ΔTR,R=LKA\frac{Q}{t} = \frac{KA\,\Delta T}{L} = \frac{\Delta T}{R}, \qquad R = \frac{L}{KA}

Common traps

Adding conductivities for slabs in series

Slabs in series carry the same heat and add their RESISTANCES, x/KA + 4x/2KA = 3x/KA. Averaging K is wrong.

Scaling the flow with the area alone

Doubling all dimensions multiplies A by 4 but also doubles L, so the flow only doubles.

Radiation: Stefan, Wien and Newton's Law of Cooling

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Stefan's Law: Power Grows as T⁴

Stefan's law

P=eσAT4,Pnet=eσA(T4−T04)P = e\sigma A T^4, \qquad P_{\text{net}} = e\sigma A\left(T^4 - T_0^4\right)

Wien's Law: the Peak Moves With Temperature

Wien's law

λmT=b,P2P1=(λm1λm2)4\lambda_m T = b, \qquad \frac{P_2}{P_1} = \left(\frac{\lambda_{m1}}{\lambda_{m2}}\right)^4

Newton's law of cooling

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

Absorbed, Reflected, Transmitted, and the Black Body

QuantityRule
Incident heatabsorbed + reflected + transmitted
Opaque bodyt = 0, a + r = 1
Perfect black bodya = 1, emissivity e = 1
Rate of cooling by colourblack > red > white
Area under the intensity–wavelength curvetotal power per unit area, all wavelengths

Common traps

Leaving out the transmitted part

a + r + t = 1 holds for any surface; only an opaque one has t = 0. Given absorbed and transmitted heat, the reflected heat is what is left.

Using degrees Celsius in T⁴

127 °C to 527 °C is 400 K to 800 K, a factor of 2 — not 527/127. Convert to kelvin before taking any power.

Ignoring the surroundings in a cooling rate

A body in surroundings at T₀ loses heat at a rate ∝ T⁴ − T₀⁴. Comparing 900 K and 600 K in a 300 K room gives 5.3, not (900/600)⁴ = 5.1.

Raising the wavelength ratio to the fourth power the wrong way

Power goes as T⁴, and T as 1/λ_m. A SHORTER peak wavelength means a hotter body and MORE power: λ/2 gives 16 times, not one sixteenth.

Forgetting the size when bodies differ

Wien fixes T, but the power also goes as the area. Discs of radii 2, 3 and 6 m peaking at 300, 400 and 500 nm are not equal; compare R²/λ_m⁴.

Using the starting temperature instead of the average

The papers' form uses the AVERAGE temperature over the interval minus the surroundings: (T₁ + T₂)/2 − T₀. Using T₁ − T₀ gives a different K.

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