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The thermal stress required to keep the length constant is given by the formula:
- $\text{Stress} = Y \alpha \Delta T$
- Substituting the values: $\text{Stress} = (2 \times 10^{11}) \times (1.1 \times 10^{-5}) \times 100$
- $\text{Stress} = 2.2 \times 10^{8}\text{ Pa}$
Pressure is equivalent to the stress applied at the ends.
For adiabatic expansion: $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$
$300 \times V^{2/3} = T_2 \times (2V)^{2/3} \implies T_2 = \frac{300}{2^{2/3}} \approx \frac{300}{1.587} \approx 189 \text{ K}$
Change in internal energy: $\Delta U = n C_v \Delta T = n \left(\frac{3}{2}R\right) (T_2 - T_1)$
$\Delta U = 2 \times 1.5 \times 8.31 \times (189 - 300) \approx 24.93 \times (-111) \approx -2767 \text{ J} \approx -2.7 \text{ kJ}$.
Which part of the brain primarily controls your sense of balance and coordination?
The cerebellum processes sensory information and coordinates voluntary movements, balance, posture, and fine motor control. Amygdala: emotion; Hippocampus: memory; Medulla: autonomic functions.
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