Calculate how much steam from water boiling at 100 C will just melt 50 gm of wax at 20 C. (Melting point of wax=55 C, sp. heat capacity of wax=0.7cal/g C, sp. latent heat of fusion of wax=35cal/g)

m₁ = 5.507 x 10⁻³ kg = 5.507 g

Explanation:

The heat released by the steam must be absorbed by the melting wax, according to the law of conservation of energy:

Heat Released by Steam = Heat Absorbed by Wax

Latent Heat of Fusion of Steam = Heat Absorbed by Wax + Latent Heat of Fusion of Wax

m₁H₁ = m₂CΔT₂ + m₂H₂

where,

m₁ = mass of water = ?

H₁ = Latent Heat of Fusion of Water = 2260 KJ/kg = 2.26 x 10⁶ J/kg

m₂ = mass of wax = 50 g = 0.05 kg

C = specific heat capacity of wax = (0.7 cal/g°C)(1000 g/1 kg)(4.184 J/1 Cal)

C = 2928.8 J/kg.°C

ΔT₂ = Change in Temperature of Wax = 55°C - 20°C = 35°C

H₂ = Latent Heat of Fusion of Wax = (35 cal/g)(1000 g/1 kg)(4.184 J/1 Cal)

H₂ = 146440 J/kg

Therefore,

m₁(2.26 x 10⁶ J/kg) = (0.05 kg)(2928.8 J/kg.°C)(35°C) + (0.05 kg)(146440 J/kg)

m₁ = (5125.4 J + 7322 J)/2.26 x 10⁶ J/kg

m₁ = 5.507 x 10⁻³ kg = 5.507 g

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min