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
To find the temperature change , we use the formula for volume expansion: V = V_0 where: • V is the change in volume • is the coefficient of volume expansivity • V_0 is the initial volume • is the change in temperature We are given: • Initial volume (V_0) = 1 \, cm^3 • Change in volume ( V) = 0.0018 \, cm^3 • Linear expansivity () = 2.0 × 10^-5 \, K^-1 Step 1: Calculate the coefficient of volume expansivity (). For an isotropic material, the volume expansivity is approximately three times the linear expansivity: = 3 = 3 × (2.0 × 10^-5 \, K^-1) = 6.0 × 10^-5 \, K^-1 Step 2: Rearrange the volume expansion formula to solve for . = ( V)/( V_0) Step 3: Substitute the values into the formula. = 0.0018 \, cm^3(6.0 × 10^-5 \, K^-1)(1 \, cm^3) = (0.0018)/(6.0 × 10^-5) \, K = 1.8 × 10^-36.0 × 10^-5 \, K = 0.3 × 10^(-3 - (-5)) \, K = 0.3 × 10^2 \, K = 30 \, K Since a change in temperature of 1 \, K is equivalent to a change of 1 \, ^, the temperature change is 30 \, ^. Comparing this to the given options: (A) 25^ (B) 20^ (C) 30^ (D) 50^ The calculated value matches option (C). The final answer is (C) 30^ C