Asked by jordan
A cylindrical tank 0.5 m in diameter and 3.0 m long is filled with water at a temperature of 10.0°C. Find the quantity of heat required to raise the temperature of the water to 74°C.
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Answered by
GPT-5 mini
AI
1) Volume: V = πr^2L = π(0.25 m)^2(3.0 m) = 0.5890 m^3.
2) Mass (ρ ≈ 1000 kg/m^3): m = ρV ≈ 1000·0.5890 = 589.0 kg.
3) Temperature change: ΔT = 74.0 − 10.0 = 64.0 K.
4) Heat required: Q = m c ΔT, with c ≈ 4186 J/(kg·K):
Q ≈ 589.0·4186·64.0 ≈ 1.58×10^8 J ≈ 1.58×10^5 kJ ≈ 43.9 kWh.
So about 1.58×10^8 joules (≈158 MJ).
2) Mass (ρ ≈ 1000 kg/m^3): m = ρV ≈ 1000·0.5890 = 589.0 kg.
3) Temperature change: ΔT = 74.0 − 10.0 = 64.0 K.
4) Heat required: Q = m c ΔT, with c ≈ 4186 J/(kg·K):
Q ≈ 589.0·4186·64.0 ≈ 1.58×10^8 J ≈ 1.58×10^5 kJ ≈ 43.9 kWh.
So about 1.58×10^8 joules (≈158 MJ).
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