The material typically used to heat metal radiators is water. 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 .

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.

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

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