A 165 g aluminum cylinder is removed from a liquid nitrogen bath, where it has b
ID: 1702946 • Letter: A
Question
A 165 g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to -196°C. The cylinder is immediately placed in an insulated cup containing 747 g of water at 15.0°C, and the system is allowed to come to equilibrium. Determine if all of the water freezes. If so, find the equilibrium temperature. If not, find the amount of water that has frozen. The average specific heat of aluminum over this temperature range is 653 J/(kg·K).
I need the answer in °C or grams please. I need the actual answer if possible please..
Thank you
Explanation / Answer
Let the final temperature be T_f = 0
heat gained by aluminium is Q_Al = m_Al c_Al ( T_f - T_0 )
= 165 *10^-3 kg * ( 653 J / kg C ) ( 0- ( -196 )
= 2.11*10^4 J
heat losses ny the water before it freezes is
Q = m _w c_w ( T_f - T_0 )
= 747 *10^-3 kg * 4186 J / kg C ( 15 C )
= 4.69*10^4 J
m_f = Q_Al - Q_w / L _f
= 2.11*10^4 J - 4.69*10^4 J / 33.5 *10^4 J
= 77.2 g
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