This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and calculate the change in temperature. The initial volume of the aluminium block is V_0 = 0.420 m^3. The initial temperature is T_0 = 298 K. The final temperature is T_f = 358 K. The change in temperature ( T) is: T = T_f - T_0 = 358 K - 298 K = 60 K Step 2: State the assumed volumetric thermal expansion coefficient for aluminium. The volumetric thermal expansion coefficient () for aluminium is not provided in the question. We will use a standard value for the linear thermal expansion coefficient of aluminium, _Al = 23 × 10^-6 K^-1. The volumetric thermal expansion coefficient is approximately three times the linear thermal expansion coefficient: _Al = 3 _Al = 3 × (23 × 10^-6 K^-1) = 69 × 10^-6 K^-1 Step 3: Calculate the increase in volume. The formula for the increase in volume ( V) due to thermal expansion is: V = V_0 _Al T Substitute the values: V = (0.420 m^3) × (69 × 10^-6 K^-1) × (60 K) V = 1738.8 × 10^-6 m^3 V = 0.0017388 m^3 Rounding to three significant figures, the increase in volume is: V = 0.00174 m^3 Send me the next one 📸