A block of ice of mass 0.8 kg and initial temperature T = 0 oC is placed in a se

Question

A block of ice of mass 0.8 kg and initial temperature T = 0 oC is placed in a sealed insulated container full of Helium gas, initially at temperature 150 oC and pressure of 1 atm. The volume of the Helium is 650 L, and is constant. Helium is a monatomic ideal gas. What is the mass of the liquid water when the system comes to equilibrium? (In other words, how much ice melts?) Assume no heat is lost to the surroundings. Give your answer in kg to three significant digits. Do not include units in your answer.

Explanation / Answer

let mass of ice that melts is m kg.

then heat transferred from the helium gas=mass of ice melted*latent heat of fusion

=334*10^3*m J

this much heat loss is used to bring the temperature of helium gas from 150 degree celcius to 0 degree celcius

now, initial pressure =1 atm=101325 Pa

volume=650 L=0.65 m^3

temperature=150 degree celcius=150+273=423 K

then number of moles=pressure*volume/(gas constant*temperature)

=101325*0.65/(8.314*423)=18.725 moles

as volume remains constant, the heat lost is equal to the decrease in intenral energy

hence change in internal energy when temperature drop from 150 degree to 0 degree celcius=number of moles*specific heat at constant volume*change in temperature

=18.725*1.5*8.314*(150-0)=3.5028*10^4 J

hence equating the energy values:

334*10^3*m=3.5028*10^4

==>m=3.5028*10^4/(334*10^3)=0.10487 kg

hence 0.10487 kg of ice has melted.

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