Using the formula $R=\frac{\Delta T}{\alpha}$ where $\alpha$ is the coefficient of thermal expansion, and $\Delta T$ is the change in temperature, how would you solve for $\Delta T$?
a. $\Delta T=R \alpha$
b. $\Delta T=R+\alpha$
c. $\Delta T=\frac{R}{a}$
d. $\Delta T=\frac{a}{R}$
Answer (2)
Start with the formula: R = α Δ T .
Multiply both sides by α to isolate Δ T : α × R = Δ T .
Therefore, Δ T = R α .
The solution for Δ T is R α .
Explanation
Understanding the Problem We are given the formula R = α Δ T and we want to solve for Δ T . This means we want to isolate Δ T on one side of the equation.
Solving for Delta T To isolate Δ T , we can multiply both sides of the equation by α . This gives us: α × R = α × α Δ T α R = Δ T So, Δ T = R α .
Final Answer Therefore, the correct answer is Δ T = R α .
Examples
In thermodynamics, this formula helps determine the change in temperature of a material when subjected to a thermal resistance. For example, if you know the thermal resistance of a window and the coefficient of thermal expansion of the glass, you can calculate how much the temperature will change when heat flows through it. This is crucial in designing energy-efficient buildings and understanding heat transfer processes.
To solve for Δ T in the equation R = α Δ T , you multiply both sides by α which gives Δ T = R α . Therefore, the correct option is (a) Δ T = R α .
;
