A water bath absorbs 8.36 kJ of heat. If a copper object has c=0.385 kJ/kgK and ΔT=30 K, what is its mass?

A water bath absorbs 8.36 kJ of heat. If a copper object has c=0.385 kJ/kgK and ΔT=30 K, what is its mass?

• A. Approximately 1.0 kg
• B. Approximately 2.0 kg
• C. Approximately 0.72 kg
• D. Approximately 0.36 kg

Answer: (C)

The heat gained by the copper relates to its mass, specific heat, and temperature change through Q = m c ΔT. Here Q is 8.36 kJ, c is 0.385 kJ/kgK, and ΔT is 30 K. Solve for mass: m = Q / (c ΔT) = 8.36 kJ / (0.385 kJ/kgK × 30 K) = 8.36 / 11.55 ≈ 0.724 kg. So the mass is about 0.72 kg. For quick checks: 0.36 kg would yield only about 4.16 kJ of heat for the same rise, 1.0 kg would require about 11.55 kJ, and 2.0 kg would need about 23.1 kJ, which don’t match the given heat.

The heat gained by the copper relates to its mass, specific heat, and temperature change through Q = m c ΔT. Here Q is 8.36 kJ, c is 0.385 kJ/kgK, and ΔT is 30 K. Solve for mass: m = Q / (c ΔT) = 8.36 kJ / (0.385 kJ/kgK × 30 K) = 8.36 / 11.55 ≈ 0.724 kg. So the mass is about 0.72 kg. For quick checks: 0.36 kg would yield only about 4.16 kJ of heat for the same rise, 1.0 kg would require about 11.55 kJ, and 2.0 kg would need about 23.1 kJ, which don’t match the given heat.