A block of ice of mass 0.6 kg and initial temperature T = 0 o C is placed in a s
ID: 1487286 • Letter: A
Question
A block of ice of mass 0.6 kg and initial temperature T = 0 oC is placed in a sealed insulated container full of Helium gas, initially at temperature 175 oC and pressure of 1 atm. The volume of the Helium is 750 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
since volume is constant so work done by helium on surrounding = 0 J
Q = w + dE
Q = 0 + dE
PV = nRT
101325 * (750 *10^(-3)) = n (8.314 ) (273+175)
n = 20.4028032535
Q = dE = 3/2 * nR dT => 3/2 * (20.4028032535) * (8.314)* dT
= 254.443359374 dT = heat loss by helium
maximum heat that can be transferred if (dT = 175)
= 254.443359374 *175
=44527.5878904 J
heat gain by ice = mL + msdT
= m* (334)
let all ice is converted to water
heat required = 0.6*1000 * 334 =>200400 J
clearly maximum heat that can be supplied by helium is less than required by ice so
let m mass of ice melts
m *(334) = (44527.5878904)
= 133.316131408 gm
= 0.133 Kg
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