Heat, temperature and thermal expansion
- A metallic bar of Young's modulus, 0.5×10^11 N m^-2 and coefficient of linear thermal expansion 10^-5 ^°C^-1, length 1 m and area of cross-section 10^-3 m^2 is heated from 0^°C to 100^°C without expansion or bending. The compressive force developed i… Answer: 3. 50×10³ N Key idea: If the bar is not allowed to expand, the thermal strain αΔ T is cancelled by a compressive strain, so a stress... 1
- A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : (α_Cu = 1.7×10^-5 K^-1 and α_Al = 2.2×10^-5 K^-1) Answer: 4. 68 cm The difference in length stays the same at all temperatures only if both rods expand by the same amount: Δ l_Cu=Δ l_Al . l_... 1
- Coefficient of linear expansion of brass and steel rods are α_1 and α_2. Lengths of brass and steel rods are l_1 and l_2 respectively. If (l_2 - l_1) is maintained same at all temperatures, which one of the following relations holds good ? Answer: 4. α₁ l₁ = α₂ l₂ Key idea: the difference of lengths stays constant only if both rods expand by the same amount. Δ l₁=Δ l₂⇒ l₁α₁Δ T=... 1