Answer to Question #141140 in Physics for Lawal waliyi

Question

a steel rod near a blacksmith furnace is 1.00m long with a mass of 1.7kg and crosectional area 0.0001. if the rod absorb 40000j. find the increas in length of the rod.

Answer 1

The equation of a termal balance here is:

$$Q = mc\Delta T$$

where $Q = 4\times 10^4J$ is the amount of heat the rod has absorbed, $m = 1.7kg$ is the mass of the rod, $c = 460J/(kg\cdot K)$ is the specific heat capacity of steel and $\Delta T$ is the increase in temperature. Thus, expressing the temperature increase, obtain:

$$\Delta T = \dfrac{Q}{mc}$$

According to the termal expansion law, the increas in length of the rod is given by:

$$\Delta L = \alpha_L\cdot L\cdot \Delta T$$

where $\alpha_L = 11\times 10^{-6}K^{-1}$ is the coefficient of linear thermal expansion of steel, $L = 1m$ is the initial length of the rod and $\Delta T$ is the increase in temperature that we have already found. Substituting the expression for $\Delta T$, obtain:

$$\Delta L = \alpha_L\cdot L\cdot \dfrac{Q}{mc}\\ \Delta L = 11\times 10^{-6}\cdot 1\cdot \dfrac{4\times 10^4}{1.7\cdot 460} \approx 5.63\times 10^{-4}m$$

Answer. $5.63\times 10^{-4}m$.