__ 8. You need to raise each beaker's temperature 10^circ C Which beaker needs the most heat to cause this temperature change? A. a beaker containing 400 mI of water at 20^circ C B. a beaker containing 400 mL of motor oil at 20^circ C. a beaker containing 800 mL of motor oil at 30^circ C D. a beaker containing 800 mL of water at 10^circ C

The amount of heat (Q) required to change the temperature of a substance is given by the equation:<br /><br />Q = mcΔT<br /><br />Where:<br /><br />* Q is the heat energy<br />* m is the mass of the substance<br />* c is the specific heat capacity of the substance<br />* ΔT is the change in temperature<br /><br />We are given that ΔT is the same for all beakers (10°C). We also know that the density of water is greater than the density of oil. Since the volumes are given in mL, and 1 mL of water has a mass of approximately 1 g, we can treat the volume of water as its mass in grams. We'll assume the density of motor oil is approximately 0.8 g/mL.<br /><br />Now let's analyze each option:<br /><br />* **A. 400 mL of water at 20°C:** m ≈ 400 g, c = 4.18 J/g°C (specific heat of water)<br />* **B. 400 mL of motor oil at 20°C:** m ≈ 400 mL * 0.8 g/mL = 320 g, c ≈ 1.7 J/g°C (specific heat of motor oil is roughly half that of water)<br />* **C. 800 mL of motor oil at 30°C:** m ≈ 800 mL * 0.8 g/mL = 640 g, c ≈ 1.7 J/g°C<br />* **D. 800 mL of water at 10°C:** m ≈ 800 g, c = 4.18 J/g°C<br /><br />Since Q is directly proportional to both mass (m) and specific heat (c), we can compare the product of m and c for each option:<br /><br />* **A:** 400 g * 4.18 J/g°C ≈ 1672<br />* **B:** 320 g * 1.7 J/g°C ≈ 544<br />* **C:** 640 g * 1.7 J/g°C ≈ 1088<br />* **D:** 800 g * 4.18 J/g°C ≈ 3344<br /><br />The beaker with 800 mL of water (D) has the highest product of mass and specific heat, therefore requiring the most heat to raise its temperature by 10°C.<br /><br />Final Answer: The final answer is $\boxed{D}$<br />