A block of ice of mass 0.9 kg and initial temperature T = 0 o C is placed in a s

Question

A block of ice of mass 0.9 kg and initial temperature T = 0 oC is placed in a sealed insulated container full of Helium gas, initially at temperature 220 oC and pressure of 1 atm.   The volume of the Helium is 680 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

we know that
P1V1/T1 = P2V2/T2
Here,V1 = V2,P1 = 1 atm,P2 =1.65 atm,T1 = 220 oC and T2 is the final temperature
or P1/T1 = P2/T2
or T2 = P2/P1 * T1 = 1.65/1 * 220 = 363 oC
the heat energy in the ice block is
Q = msdelta(t)
where m = 0.9 kg,s is specific heat of ice and delta(t) = 363- 220=143 oC
the latent heat of ice is
Q1 = m1 * L
where m1 is amount of ice which melts and L is latent heat of fusion of ice
HereQ = Q1

specific heat of water= 1.00 (cal/gC)

latent heat of fusion for ice= 79.6 (cal/g)

or msdelta(t) = m1 * L
or m1 = msdelta(t)/L
     = 900g*2.03Jg/C*143C / 334J/g
= 782g
= 0.782kg

Answer=0.782

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