How much water vapor is required at a temperature of 100 ° C to heat a 200 kg

How much water vapor is required at a temperature of 100 ° C to heat a 200 kg concrete slab from a temperature of 10 ° C to a temperature of 40 ° C?

mb = 200 kg.

t1 = 10 ° C.

t2 = 40 ° C.

t3 = 100 ° C.

C = 1130 J / kg * ° С.

r = 2.3 * 10 ^ 6 J / kg.

mp -?

The amount of heat Q that is needed to heat concrete is determined by the formula: Q = C * mb * (t2 – t1), where C is the specific heat capacity of concrete, mb is the mass of the concrete slab, t2, t1 are the final and initial temperatures of the slab.

Since water vapor is at a boiling point of t3 = 100 ° C, the amount of heat Q that is released during its condensation is determined by the formula: Q = r * mp, where r is the specific heat of vaporization of water, mp is the mass of steam.

C * mb * (t2 – t1) = r * mp.

mp = C * mb * (t2 – t1) / r.

mp = 1130 J / kg * ° C * 200 kg * (40 ° C – 20 ° C) / 2.3 * 10 ^ 6 J / kg = 1.97 kg.

Answer: to heat a concrete slab, you need mp = 1.97 kg of water vapor.