InterviewSolution
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InterviewSolution
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A thermally isulated piece of metal is heated under atmospheric pressure by an electric current so that it receives electric energy at a constant power P. This leads to an increase of absolute temperature T of the metal with time t as follows: `T(t)=T_0[1+a(t-t_0)]^(1//4)`. Here, a, `t_0` and `T_0` are constants. The heat capacity `C_p(T)` of the metal isA. `(4P)/(aT_0)`B. `(4PT)/(aT_0^4)`C. `(2PT)/(aT_0^4)`D. `(2P)/(aT_0)` |
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Answer» Correct Answer - B Heat given to the metal `dQ=Pdt=C_P(t)dT` ..(i) At constant pressure in time interval at Given `T=T_0[1+a(t-t_0)]^(1//4)` `(dT)/(dt)=(T_0)/(4)[1+a(t-t_0)^(-3//4)xxa` ..(ii) From Eqs. (i) and (ii) `C_P(T)=(P)/(((dT)/(dt)))=(4P[1+a(t-t_0)]^(3//4))/(T_0a)=(4PT^3)/(aT_0^4)` |
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