Joule, mixed, 1 (thermo-05) You mix 1 kg of melting ice and 1 kg of sitting ice. What is the temperature of the mixture when all the ice has melted?

  Exercise: thermo-05    

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You mix 1 kg of melting ice and 1 kg of sitting ice. What is the temperature of the mixture when all the ice has melted?

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Solution:

1. Basic idea: Hot water cools, cold water warms
2. The following abbreviations apply: H for hot, K for cold, M for mixture
3. The ice must first be melted (L_f is the energy required) and can then only be heated to the mixture temperature
4. Q(100℃ → T_M) = Q(Eis schmelzen, 0℃ → T_M)
5. m_H · c_w · (100℃ – T_M) = m_K·L_f + m_K · c_w · (T_M – 0℃ )
6. Converting Celsius to Kelvin, m_H = m_K = m
7. m·c_w·(373K-T_M) = m·L_f +m·c_w·(T_M-273K)
8. T_M = [c_w·(373k+273k)-L_f]/(2·c_w)
9. T_M = [4.185kJ/kgK·(373k+273k)-335.5kJ]/(2·4.185kJ/kgK) = 283.2 K = 10.2℃

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