Complete question:
The material typically used to heat metal radiators is water. 4.05 x 10⁵ J of heat must be supplied to the radiator in order to raise its temperature from 25.0 to 55.0°C. If a boiler generates water at 84.0°C, what mass of water is required to heat the radiator? Water has a specific heat of 4.184 J.g⁻¹.C⁻¹.
Answer:
The mass of water required to heat the radiator is 3.338 kg
Explanation:
Given;
Quantity of heat supplied to raise the temperature of radiator, Q = 4.05 x 10⁵ J
Specific heat capacity of water, c = 4.184 J.g⁻¹.C⁻¹ = 4.184 x 10³ J.kg⁻¹C⁻¹
Quantity of heat supplied to raise the temperature of water;
Q = mcΔθ
where;
m is the mass of water
c is the specific heat capacity of water
Δθ is the temperature difference of water from 84.0°C to 55.0°C
m = Q / cΔθ , Δθ = 84.0°C - 55.0°C = 29°C
m = (4.05 x 10⁵ ) / (4.184 x 10³ x 29)
m = 3.338 kg
Therefore, the mass of water required to heat the radiator is 3.338 kg
The mass of the water needed to heat the radiator is 3338 g
We'll begin by calculating the change in the temperature of the water.
Initial temperature of water (T₁) = 84 °C
Final temperature (T₂) = 55 °C
ΔT = T₂ – T₁
ΔT = 55 – 84
Heat released (Q) = –4.05×10⁵ J
Change in temperature (ΔT) = –29 °C
Specific heat capacity of water (C) = 4.184 J/gºC
Q = MCΔT
–4.05×10⁵ = M × 4.184 × –29
–4.05×10⁵ = M × –121.336
Divide both side by –121.336
M = –4.05×10⁵ / –121.336
Therefore, the mass of the water needed to heat the radiator is 3338 g
The material typically used to heat metal radiators is water. 4.05 x 10⁵ J of heat must be supplied to the radiator in order to raise its temperature from 25.0 to 55.0°C. If a boiler generates water at 84.0°C, what mass of water is required to heat the radiator? Water has a specific heat of 4.184 J.g⁻¹.C⁻¹.
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