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Je m'appelle
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Homework Statement
The molar heat capacity at a constant volume of a solid at low temperatures T << Td, where Td is the Debye temperature is given by:
[tex]C_v = 464(\frac{T}{T_d})^3 [/tex]
Consider Td = 281 K for the NaCl.
(a) Calculate the average molar heat capacity [tex]\bar{C_v}[/tex] of the NaCl between the temperatures of Ti = 10 K and Tf = 20 K.
(b) Calculate the amount of heat necessary to raise the temperature of 1,000g of NaCl from 10 K to 20 K.
Homework Equations
[tex]C_v = 464(\frac{T}{T_d})^3 [/tex]
[tex]C_v = (\frac{\delta Q}{dT})_v[/tex]
The Attempt at a Solution
(a) So I found the heat capacities Ci and Cf at Ti and Tf, respectively, and then in order to find the average heat capacity I summed them and divided by 2.
[tex]C_i = 464(\frac{10}{281})^3 [/tex]
[tex]C_i = 0,021 [/tex]
[tex]C_f = 464(\frac{20}{281})^3 [/tex]
[tex]C_f = 0,167 [/tex]
[tex]\bar{C_v} = \frac{C_i + C_f}{2} [/tex]
[tex]\bar{C_v} = 0,94 [/tex]
Is this correct?
(b)
[tex](\frac{\delta Q}{dT})_v = C_v [/tex]
[tex]\delta Q = \bar{C_v} dT [/tex]
[tex]\delta Q = (0,94)(10) = 9,4 [/tex]
Is this also correct?
Thanks.