Thermodynamics Question 312
Question: The molar heat capacity of a certain substance varies with temperature according to the given equation, $ C=27.2+(4\times {{10}^{-3}})T. $ The heat necessary to change the temperature of 2 mol. of the substance from 300K to 700K is
Options:
A) $ 3.46\times 10^{4}J $
B) $ 2.33\times 10^{3}J $
C) $ 12\times 10^{5} $
D) $ 2.33\times 10^{4}J $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Initial temperature, $ T _{i}=300K; $
Final temperature, $ T _{f}=700K $
$ Q=\int\limits _{300}^{700}{nCdT=\int\limits _{300}^{700}{2\times (27.2+4\times {{10}^{-3}}\times T)dT}} $
$ =[ 54.4T+4\times {{10}^{-3}}T^{2} ] _{300}^{700}=2.33\times 10^{4}J $
