The heat required to raise the temperature of 2 kg of water by 20 K (c = 4184 J/kg·K) is approximately what value?

The heat required to raise the temperature of 2 kg of water by 20 K (c = 4184 J/kg·K) is approximately what value?

• A. 8.4 × 10^4 J
• B. 1.67 × 10^5 J
• C. 1.0 × 10^5 J
• D. 2.0 × 10^5 J

Answer: (B)

The amount of heat needed to raise a substance’s temperature is Q = m c ΔT. For water, c is 4184 J/(kg·K). With a mass of 2 kg and a temperature rise of 20 K, the heat required is Q = 2 × 4184 × 20 = 167,360 J, about 1.67 × 10^5 J (0.167 MJ). This matches the given value for a 20 K increase with 2 kg of water. Noting the others helps: a value around 8.4 × 10^4 J would correspond to a 10 K rise, about 1.0 × 10^5 J to roughly 12 K, and 2.0 × 10^5 J to roughly 24 K.

The amount of heat needed to raise a substance’s temperature is Q = m c ΔT. For water, c is 4184 J/(kg·K). With a mass of 2 kg and a temperature rise of 20 K, the heat required is Q = 2 × 4184 × 20 = 167,360 J, about 1.67 × 10^5 J (0.167 MJ). This matches the given value for a 20 K increase with 2 kg of water.

Noting the others helps: a value around 8.4 × 10^4 J would correspond to a 10 K rise, about 1.0 × 10^5 J to roughly 12 K, and 2.0 × 10^5 J to roughly 24 K.