Related Formula
Thermal Tension, T = Y A α Δ θ$$\text{Thermal Tension, } T = Y A \alpha \Delta \theta$$
Core Logic
For the first cooling, the tension T$T$ generated is:
T = Y A α Δ θ₁$$T = Y A \alpha \Delta \theta_1$$
T = Y A α (27 - (-43))$$T = Y A \alpha (27 - (-43))$$
T = Y A α (70) (i)$$T = Y A \alpha (70) \quad \dots \text{(i)}$$
Let θ$\theta$ be the final temperature required for a tension of 1.4T$1.4T$.
1.4T = Y A α (27 - θ) (ii)$$1.4T = Y A \alpha (27 - \theta) \quad \dots \text{(ii)}$$
Step 1: Ratio of Tensions
Dividing equation (ii) by equation (i):
(1.4T)/(T) = (27 - θ)/(70)$$\frac{1.4T}{T} = \frac{27 - \theta}{70}$$
1.4 = (27 - θ)/(70)$$1.4 = \frac{27 - \theta}{70}$$
27 - θ = 1.4 × 70 = 98$$27 - \theta = 1.4 \times 70 = 98$$
θ = 27 - 98 = -71° C$$\theta = 27 - 98 = -71^{\circ} \text{C}$$
Pattern Recognition
Thermal tension strictly scales with the absolute difference in temperature from the unstressed state, Δ θ$\Delta \theta$. Multiplying tension by a factor simply scales Δ θ$\Delta \theta$ by that identical factor.
Chapter Mix
Class 11 Physics: Mechanical Properties of Solids
Class 11 Physics: Thermal Properties of Matter