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: Calculate the change in temperature. The initial temperature is 52 \, ^ C and the final temperature is 100 \, ^ C. T = T_final - T_initial = 100 \, ^ C - 52 \, ^ C = 48 \, ^ C Since a change in Celsius is equivalent to a change in Kelvin, T = 48 \, K. Step 2: Calculate the heat energy required to boil the water. The mass of the water is m = 2.5 \, kg, and the specific heat capacity of water is c = 4.2 × 10^3 \, Jkg^-1K^-1. The heat energy Q is given by the formula Q = mc T. Q = (2.5 \, kg) · (4.2 × 10^3 \, Jkg^-1K^-1) · (48 \, K) Q = 2.5 × 4.2 × 48 × 10^3 \, J Q = 10.5 × 48 × 10^3 \, J Q = 504 × 10^3 \, J Q = 5.04 × 10^5 \, J Step 3: Calculate the electrical power of the immersion heater. The immersion heater is rated at I = 2.0 \, A and V = 240 \, V. The electrical power P is given by the formula P = VI. P = (240 \, V) · (2.0 \, A) P = 480 \, W Step 4: Calculate the time taken to boil the water. Assuming all the electrical energy is converted into heat energy, the heat energy supplied by the heater is Q = P · t, where t is the time taken. Rearranging for t: t = (Q)/(P) t = (5.04 × 10^5 \, J)/(480 \, W) t = (504000 \, J)/(480 \, W) t = 1050 \, s Step 5: Express the time in scientific notation and compare with options. t = 1.05 × 10^3 \, s Comparing this with the given options: (a) 1.05 × 10^3 \, s (b) 1.05 × 10^3 \, s (c) 1.05 × 10^2 \, s (d) 0.105 × 10^4 \, s = 1.05 × 10^3 \, s Options (a), (b), and (d) are numerically identical. We will select option (a). The final answer is A. 1.05 × 10^3 s.