An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$, and Youngâ€™s modulus $E$ is fixed at the two ends. The temperature of the bar is increased by $T$, resulting in an axial stress $\sigma$. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

- $\sigma$
- $2 \: \sigma$
- $0.5 \: \sigma$
- $0.25 \: \alpha \: \sigma$